Just look at his Wikipedia entry. He finished his dissertation in 1955, starting teaching at MIT the same year, and continued to publish seminal linguistic works over the next 12 years. That's all before he gained any notoriety whatsoever as a critic of the U.S.'s role in the Vietnam War.

Manufacturing Consent was published in 1988!

Additionally, I strongly doubt Chomsky had any "name recognition" all the way through to the late 90s. Outside of a single episode of Firing Line, where would the general public have heard his views?