By all reports, Chomsky was a very captivating speaker during the Anti-Vietnam War protests in the 1960s.  Pieces I've read by eyewitness report that he had apparently already developed his distinctive rhetorical style of delivering very devastating information in a very detached and academic tone--which was to characterize all his media appearances in the 70s and 80s.

Unfortunately, it's very hard to find audio from those speeches in the 1960s.  (I'm assuming this was because he had not yet become the cult figure on the left that he is today, and so very few people thought to make audio recordings).

But I did find one recording on Youtube the other day, and it's worth listening to--not only as a historical time piece, but as a remarkable demonstration of Chomsky's rhetorical appeal:



The only other Chomsky piece from the 1960s I'm aware of is his debate with William F. Buckley.  I've linked to it before (twice, actually), but I'll repost it here anyway.