Talk show. (Thanks to Gigi Simeone.) “It came under immediate and sustained attack on the weekend political chat shows” (Hendrik Hertzberg, The New Yorker, June 14, 2004)/”If [New Jersey Governor Chris Christie] is not at a town-hall-style forum, it seems, he is on a television chat show.” (New York Times, March 10, 2011) Google Ngram.
notoneoffbritishisms.com 
I was always under the impression that chat shows and talk shows are different. Craig Ferguson/Jonathan Ross = chat show. Jerry Springer/Matthew Wright = talk show
doesn’t Jagger sing “and your mother was a chat show queen” in the Stones “Brown Sugar”? and I am sure he was in American mode, not UK
“Tent show queen,” according to my sources. (If you were joking, my bad.)
DIsagree with Psi. I do not believe that ‘talk show’ is used in BrE, and if it is, it will be an Americanism. Over here, a talk is generally more serious than a chat. We ‘give talks’ (ie lectures), give someone a ‘talking to’ (tell them off), and can ‘talk down to’ and ‘across’ people. ‘Speak’ can be worse, as in I’m going to speak to (not with) your mother/father/headmaster’. On the other hand, a chat is much more informal and friendly. These terms are not interchangeable. So ‘talk show’ would probably lead a Brit to expect an oral presentation, unlike a chat show that would featur people talking informally together. Personally I wouldn’t categorise Jerry Springer or Matthew Wright as either. Wikipedia calls the Mathew Wright show a ‘topical discussion series’, where ‘topical’ may be a euphemism for ‘ratings-seeking’ and ‘discussion’ for ‘ego-airing’. Those shows are issue-based, unlike a chat show, which is celebrity-based.