Chomsky was raised Jewish but now considers himself an atheist.
Chomsky is an anarcho-syndicalist and a socialist libertarian.
Noam Chomsky was born and raised in Philadelphia, Pennsylvania.
Chomsky's religious and biological heritage is Jewish. He has spoken often about experiencing and enduring antisemitism growing up, but now–rather controversially–asserts that antisemitism in the U.S. has all but disappeared, except to spring up when the powers that be want to make sure they still have the power:
Anti-semitism is no longer a problem. It's raised, but it's raised because privileged people want to make sure they have total control, not just 98% control.
Something one must understand about Chomsky if they are to understand the millions upon millions of words that have escaped his mouth and been recorded: He views the world as exceedingly complex, that there are no simple answers, and that he could be quite wrong at any given time–though he doesn't usually think he is. He is what some may call a perspective centered person.
That being said, he is an atheist and his condemnation of religion has been scathing:
How do I define God? I don't. Divinities have been understood in various ways in the cultural traditions that we know. Take, say, the core of the established religions today: the Bible. It is basically polytheistic, with the warrior God demanding of his chosen people that they not worship the other Gods and destroy those who do — in an extremely brutal way, in fact. It would be hard to find a more genocidal text in the literary canon, or a more violent and destructive character than the God who was to be worshiped.
Still, in classic perspective-centered fashion, Chomsky admits that religion can be a powerful force for good, offering community, solidarity, and comfort for people. More recently, he praised some aspects of the Catholic Church for it's "radical" politics and its attempt to push south and Central American society in a more cooperative and humanitarian direction.
Anarcho-syndicalism and social libertarianism
That's a mouthful, eh?
Chomsky is one of the west's foremost political and social critics. His views on society, modern power structures, governance, and foreign relations is colored by a decades-long career of commentary, activism, writing, and public speaking. To fully grasp Chomskyism would require extensive study, much more then can be offered here.
While Chomsky is a darling of America's political left, his views are much more radical (by conventional standards) than many contemporary liberals would be comfortable with–if only they truly understood them!
In essence, Chomsky could be said to value personal freedom, self-governance, and participation and engagement in government above all else. He has called himself a "child of the Enlightenment" because he champions reason and a faith in the individual over institutionalized fear and superstition.
If we must label Chomsky, we can go with the labels he has given himself: Anarcho-Syndicalist and libertarian socialist. This, in an over-simplified nutshell, means that people could govern themselves with a combination of labor associations and direct democracy, and no formal government would be required. He has said, and pardon the long quote:
Now a federated, decentralized system of free associations, incorporating economic as well as other social institutions, would be what I refer to as anarcho-syndicalism; and it seems to me that this is the appropriate form of social organization for an advanced technological society in which human beings do not have to be forced into the position of tools, of cogs in the machine. There is no longer any social necessity for human beings to be treated as mechanical elements in the productive process; that can be overcome and we must overcome it to be a society of freedom and free association, in which the creative urge that I consider intrinsic to human nature will in fact be able to realize itself in whatever way it will.
There is much to learn from and know about Noam Chomsky. I highly recommend that you don't stop here and make an attempt to fully understand the nuance and brilliance of this great mind who, whether or not you agree with him, will certainly have a permanent place in the history of our era's great thinkers.