CBS We're less than two weeks away from the final episode of The Late Show. The CBS late-night talk show, hosted by Stephen Colbert, will be airing its final episode on Thursday, May 21. Ahead of the final episode, The Wrap has learned that Jimmy Kimmel Live! will be taking the night off on the 21st and will not be airing a new episode. Instead, a rerun episode of the ABC show will air. Since The Late Show and Jimmy Kimmel Live! air at the same time, 11:35pm ET, this will leave Colbert with one less competitor as he brings his show to a close after CBS canceled it last year.