Receiving his Ph.D in linguistics from Penn in 1955, Chomsky had conducted most of his research the previous four years at Harvard University as a Harvard Junior Fellow. In his doctoral thesis, he began to develop some of his linguistic ideas, elaborating on them in his 1957 book Syntactic Structures, perhaps his best known work in linguistic field.
After receiving his doctorate, Chomsky taught at the Massachusetts Institute of Technology for 19 years, receiving the first award from the Ferrari P. Ward Chair of Modern Languages and linguistics. It was during this time that Chomsky became more publicly engaged in politics, arguing against American involvement in the Vietnam War from around 1964. In 1969, Chomsky published American Power and the New Mandarins, a book of essays also on the Vietnam War. Since that time, Chomsky has become well known for his political views, speaking on politics all over the world, and writing several other books on the subject. His beliefs, broadly classified as libertarian socialism, have earned him both a large following among the left, as well as many detractors on all sides of the political spectrum. He has continued to write and teach on linguistics also.
Recent theories of Chomsky's (such as his Minimalist Program) make strong claims regarding universal grammar — that the grammatical principles underlying languages are completely fixed and innate, and the differences among the world's languages can be characterized in terms of parameter settings in the brain (such as the pro-drop parameter, which indicates whether an explicit subject is always required, as in English, or can be optionally dropped, as in Spanish), which are often likened to switches. (Hence the term principles and parameters, often given to this approach.) In this view, a child learning a language need only acquire the necessary lexical items (words) and morphemes, and determine the appropriate parameter settings, which can be done based on a few key examples.
This approach is motivated by the astonishing pace at which children learn languages, the similar steps followed by children all across the world when learning languages, and the fact that children make certain characteristic errors as they learn their first language, whereas other seemingly logical kinds of errors never occur (and, according to Chomsky, should be attested if a purely general, rather than language-specific, learning mechanism is being employed).
Chomsky's ideas have had a strong influence on researchers investigating language development in children, but most researchers who work in this area do not support Chomsky's theories, often preferring emergentist or connectionist theories based around general processing mechanisms in the brain. However, this is true of researchers in almost any branch of linguistics, and there is ongoing work on language acquisition from a Chomskyan perspective.
The Chomskyan approach towards syntax, often termed generative grammar, though quite popular, has been challenged by many, especially those working outside of the United States. Chomskyan syntactic analyses are often highly abstract, and are based heavily on careful investigation of the border between grammatical and ungrammatical constructs in a language. (Compare this to the so-called pathological cases that play a similarly important role in mathematics.) Such grammaticality judgments can only be made accurately by a native speaker, however, and thus for pragmatic reasons such linguists usually (but by no means exclusively) focus on their own native languages or languages in which they are fluent, usually English, French, German, Dutch, Italian, Japanese or one of the Chinese languages. Sometimes generative grammar analyses break down when applied to languages which have not previously been studied, and many changes in generative grammar have occurred due to an increase in the number of languages analysed. However, the claims made about language universals have become stronger rather than weaker over time; for example Kayne's suggestion in the 1990s that all languages have an underlying Subject-Verb-Object word order would have seemed implausible in the 1960s. One of the prime motivations behind an alternative approach, the functional-typological approach or linguistic typology (often associated with Joseph H. Greenberg), is to base hypotheses of linguistic universals on the study of as wide a variety of the world's languages as possible, classifying the variation seen, and forming theories based on the results of this classification. The Chomskyan approach is too in-depth and reliant on native speaker knowledge to follow this method, though it has over time been applied to a broad range of languages.
Chomsky is famous for investigating various kinds of formal language, and whether or not they might be capable of capturing key properties of human language. His Chomsky hierarchy partitions formal grammars into classes with increasing expressive power, i.e. each successive class can generate a broader set of formal languages than the one before. Interestingly, Chomsky argues that modelling some aspects of human language requires a more complex formal grammar (as measured by the Chomsky hierarchy) than modeling others. For example, while a regular language is powerful enough to model English morphology, it is not powerful enough to model English syntax. In addition to being relevant in linguistics, the Chomsky hierarchy has also become important in computer science (especially in compiler construction), as it has important ties to and isomorphisms with automata theory.
His seminal work in phonology was The sound pattern of English. He published it together with Morris Halle. This work is considered outdated (though it has recently been reprinted), and he does not publish on phonology anymore.
In 1959, Chomsky published a long-circulated critique of B.F. Skinner's Verbal Behavior, a book in which the leader of the behaviorist psychologists that had dominated psychology in the first half of the 20th century argued that language was merely a "behavior." Skinner argued that language, like any other behavior — from a dog salivating in anticipation of dinner, to a master pianist performance — could be attributed to "training by reward and penalty over time." Language, according to Skinner, was completly learned by cues and conditioning from the world around the language-learner.
Chomsky's critique of Skinner's methodology and basic assumptions paved the way for a revolution against the behaviorist doctrine that had governed psychology. In his 1966 Cartesian Linguistics and subsequent works, Chomsky laid out an explanation of human language faculties that has become the model for investigation in other areas of psychology. Much of the present conception of how the mind works draws directly from ideas that found their first persuasive author of modern times in Chomsky.
There are three key ideas. First, is that the mind is "cognitive", or that the mind actually contains mental states, beliefs, doubts, and so on. The former view had denied even this, arguing that there were only "stimulus-response" relationships like "If you ask me if I want X, I will say yes". By contrast, Chomsky showed that the common way of understanding the mind, as having things like beliefs and even unconscious mental states, had to be right. Second, he argued that large parts of what the adult mind can do are "innate". While no child is born automatically able to speak a language, all are born with a powerful language learning ability which allows them to soak up several languages very quickly in their early years. Subsequent psychologists have extended this thesis far beyond language; the mind is no longer considered a "blank slate" at birth.
Finally, Chomsky made the concept of "modularity" a critical feature of the mind's cognitive architecture. The mind is composed of an array of interacting, specialized subsystems with limited flows of inter-communication. This model contrasts sharply with the old idea that any piece of information in the mind could be accessed by any other cognitive process (optical illusions, for example, cannot be "turned off" even when they are known to be illusions).
The 1984 Nobel Prize laureate in Medicine and Physiology, Niels K. Jerne, used Chomsky's generative model to explain the human immune system,
equating "components of a generative grammar ... with various features of
protein structures". The title of Jerne's Stockholm Nobel lecture was "The Generative Grammar of the Immune System".
"I have spent a lot of my life working on questions such as these, using the only methods I know of; those condemned here as "science," "rationality," "logic," and so on. I therefore read the papers with some hope that they would help me "transcend" these limitations, or perhaps suggest an entirely different course. I'm afraid I was disappointed. Admittedly, that may be my own limitation. Quite regularly, "my eyes glaze over" when I read polysyllabic discourse on the themes of poststructuralism and postmodernism; what I understand is largely truism or error, but that is only a fraction of the total word count. True, there are lots of other things I don't understand: the articles in the current issues of math and physics journals, for example. But there is a difference. In the latter case, I know how to get to understand them, and have done so, in cases of particular interest to me; and I also know that people in these fields can explain the contents to me at my level, so that I can gain what (partial) understanding I may want. In contrast, no one seems to be able to explain to me why the latest post-this-and-that is (for the most part) other than truism, error, or gibberish, and I do not know how to proceed."
Chomsky notes that critiques of "white male science" are much like the anti-Semitic and politically motivated attacks against "Jewish physics" used by the Nazis to denigrate research done by Jewish scientists during the Deutsche Physik movement:
"In fact, the entire idea of "white male science" reminds me, I'm afraid, of "Jewish physics." Perhaps it is another inadequacy of mine, but when I read a scientific paper, I can't tell whether the author is white or is male. The same is true of discussion of work in class, the office, or somewhere else. I rather doubt that the non-white, non-male students, friends, and colleagues with whom I work would be much impressed with the doctrine that their thinking and understanding differ from "white male science" because of their "culture or gender and race." I suspect that "surprise" would not be quite the proper word for their reaction." 
Chomsky has also stated that he considers himself to be a conservative (Chomsky's Politics, pp. 188) presumably of the classical liberal variety. He has further defined himself as a Zionist; although, he notes that his definition of Zionism is considered by most to be anti-Zionism these days; the result of what he perceives to have been a shift (since the 1940s) in the meaning of Zionism (Chomsky Reader). In a C-Span Book TV interview, he stated:
"I have always supported a Jewish ethnic homeland in Palestine. That is different from a Jewish state. There's a strong case to be made for an ethnic homeland, but as to whether there should be a Jewish state, or a Muslim state, or a Christian state, or a white state — that's entirely another matter."
Overall, Chomsky is not fond of traditional political titles and categories and prefers to let his views speak for themselves. His main modes of actions include writing magazine articles and books and making speaking engagements. He has a large following of supporters worldwide, leading him to schedule speaking engagements sometimes up to two years in advance. He was one of the main speakers at the 2002World Social Forum.
Chomsky has criticized the government for its involvement in the Vietnam War and the larger Indochina conflict, as well as its interference in Central and South American countries and its military support of Israel, Saudi Arabia, and Turkey. Chomsky focuses his most intense criticism on official friends of the United States government while criticizing official enemies like the former Soviet Union and the North Vietnam only in passing. He explains this by the following principle: it is more important to evaluate actions which you have more possibility of affecting. His criticism of the former Soviet Union and China must have had some effect in those countries; both countries banned his work from publication.
Chomsky has repeatedly emphasized his theory that much of the United States' foreign policy is based on the "threat of a good example" (which he says is another name for the domino theory). The "threat of a good example" is that a country could successfully develop independently from capitalism, and the United States' influences, thus presenting a model for other countries, including countries in which the United States has strong economic interests. This, Chomsky says, has prompted the United States to repeatedly intervene to quell "socialist" or other "independence" movements in regions of the world where it has no significant economic or safety interests. In one of his most famous works, What Uncle Sam Really Wants, Chomsky uses this particular theory as an explanation for the United States' interventions in Guatemala, Laos, Nicaragua, and Grenada.
Chomsky believes the US government's Cold War policies were not entirely shaped by anti-Soviet paranoia, but rather to preserve the United States' ideological and economic dominance in the world. As he wrote in Uncle Sam: "...What the US wants is 'stability,' meaning security for the "upper classes and large foreign enterprises."