Chomsky is a very famous leftist (an anarcho-syndicalist) that is a former MIT Institute Professor that did foundational linguistics research and also made his bones protesting the Vietnam war. He writes voluminously on topics like the manufacturing of consent for war in the media, who has power, inequality, the role of science, the role of the state and market in science, and capitalism. In recent years, he has made a big point to talk about nuclear war, climate change, and the decline of democracy -- crises that threaten the world. During the 2020 election, he said to vote blue no matter who.
On the left, Norman Finkelstein, a former protegee, noted that Chomsky became known for an approach to politics and history that was very empirical at a time when many communists were very dogmatic and missed certain predictions about Maoist China. In my opinion however, Chomsky is also dogmatically anti-Marxist-Leninist to the point of caricature. I suspect that is how he retains his position in high society.