The most common and most likely answer to this crossword clue is the 3 letter word YAK
I've seen this crossword clue in The Times
Y
A
K
Buddy explains!

The straight part
We know that "Chat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case chat = yak.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does YAK mean?
YAK noun- An ox-like mammal native to the Himalayas, Mongolia, Burma, and Tibet with dark, long, and silky hair, a horse-like tail, and a full, bushy mane.
- A talk, particular an informal talk; chattering; gossip.
- A laugh.
- Vomit.
- To talk, particularly informally but persistently; to chatter or prattle.
- To vomit, usually as a result of excessive alcohol consumption.
- A kayak.