This Spring, Noam Chomsky gave four classes about syntax (and about the language faculty, and the state of the field, and …). Video of these lectures are now available. (Note: during one of them, he lost his microphone for a while — apologies in advance for the loss of sound.)
Lecture 1 (March 3, 2014)
Lecture 2 (April 2, 2014)
Lecture 3 (April 11, 2014)
Lecture 4 (May 19, 2014)
Further, Chomsky visited Sophia University and Keio University in Japan in March. Videos of lectures he gave there are available from their respective webpages.