Wikipedia, Noam Chomsky is a, "linguist, philosopher, cognitive scientist, logician, historian, political critic, activist," and a professor at MIT. I'm somewhat baffled at the cognitive scientist claim because from my perspective Chomsky seems to be engaging in cognitive dissonance. Aside from his famous quotation among Austro-libertarians that "people like Murray Rothbard... if you just read the world that they describe, it's a world so full of hate that no human being would want to live in it," he has written a book on the nature of the state entitled Government in the Future.
Based on a lecture he gave at the Poetry Center in New York City in 1970, this short book introduces the reader to Chomsky's own political worldview. Despite his excellent critiques of US foreign policy, the corporate state, and the media establishment in the last chapter, the first part of the book highlights his linguistic background, although indirectly. By twisting the definitions of classical liberalism and libertarianism to meet his end, he has crafted... well, a world so full of absurdities that no human being would want to live in it.
Chomsky cites Wilhelm von Humboldt's Limits of State Action as the de facto basis for classical liberalism. Quoting Humboldt he writes that the state, "make[s] man an instrument to serve its arbitrary ends, overlooking his individual purposes." Chomsky is in agreement with all libertarians/anarchists that the state is an anti-social organization that is "ultimately incompatible with the full harmonious development of human potential"
The problems start to arise when Chomsky regards human potential not as the typical voluntary exchanges, contracts and associations in a market economy but as some vague description of a man who "in his own terms [becomes] an artist rather than a tool of production." This misconception arises from Humboldt's theory of exploitation and alienation of labour. Hence Chomsky's view that "classical liberal ideas in their essence... are profoundly anticapitalist." 
Throughout the book, Chomsky embarrasses himself with economic illiteracy. He regards the "classical" free market as a "irrational and destructive" force. He envisions a society that will "transform the proletariat into free men by eliminating the commodity character of labor, ending wage slavery, and bringing the commercial, industrial, and financial institutions under democratic control." 
It is through this lens that Chomsky writes, "I think that the libertarian socialist concepts... are fundamentally correct and that they are the proper and natural extensions of classical liberalism into the current era of advanced industrial society." Thus, "classical libertarian thought seems to me, therefore, to lead directly to libertarian socialism or anarchism if you like, when combined with an understanding of industrial capitalism."[8, emphasis mine]
At this point, Chomsky has revealed that he has no understanding of "industrial" capitalism whatsoever. To subscribe to the theory of exploitation, one must accept the labour theory of value, which Chomsky apparently does.
Because he reasons from a false premise - that classical liberalism is anti-capitalist - his conclusion that libertarianism, or anarchism, must be anti-capitalist are wrong. "A consistent anarchist must oppose private ownership of the means of production," he writes while citing Lenin's State and Revolution as "his most libertarian work." Obviously, he doesn't even mention the economic calculation problem.
In conclusion, Chomsky regards "the problem of how to organize industrial society on truly democratic lines, with democratic control in the workplace as well as in the community," as the "dominant intellectual issue for those who are alive to the problems of contemporary society." If only he actually read Rothbard's Man, Economy and State then he would understand how the free market is, essentially, democratic. For every individual votes with each decision they make in an unhampered market economy. It is state intervention that creates social conflict. Despite this, Chomsky regards state intervention as "an absolute necessity to preserve human existence and prevent the destruction of the physical environment."
Some anarchist he is.
Chomsky's "libertarian socialism" is just another word for anarcho-syndicalism. Chomsky writes that,
State power must be eliminated in favor the democratic organization of industrial society, with direct popular control over all institutions by those who participate in - as well as those who are directly affected by - the workings of these institutions. So one might imagine a system of workers' councils, consumers' councils, commune assemblies, regional federations and so on..."
One does not need to imagine. Anarcho-syndicalism was practised during the Spanish Civil War where "democratic councils" soon became states and exercised totalitarian control over every aspect of life. The superiority of the Rothbardian anarchist society is that if Chomsky and a bunch of leftists want to try out anarcho-syndicalism again, they are free to, provided they abide by the non-aggression principle thus allowing private property capitalists to live peacefully alongside their communist neighbours. However it seems unlikely that anarcho-syndicalists would allow private property to exist anywhere because as Proudhon famously said, and Chomsky agrees  - private property is theft.
Chomsky, Noam. Government in the Future. New York: Seven Stories Press, 2005. Print.
 - pg 9
 - pg 10
 - pg 13
 - pg 15
 - pg 17
 - pg 19
 - pg 8
 - pg 23
 - pg 24
 - pg 26
 - pg 30
 - pg 16
 - pg 35-36
 - pg 24