What was the late night tv show in where host always drunk?

You're likely thinking of "The Late Show with David Letterman". While David Letterman was known for his dry wit and sarcastic humor, he was not known for being drunk on the show.

However, there have been other late-night hosts who have been rumored to be under the influence, though none have been publicly confirmed.

Is there any more information you can provide about the show or host that might help pinpoint the specific show you're thinking of?