Conversation so far:
When did he start working with Chet Baker?
During the Monday night jam sessions, a young trumpeter named Chet Baker began sitting in with Mulligan.
Mulligan and Baker began recording together.
When did they form the quartet?
These three informal sessions took place in June, July, and August 1952.
What instruments were in the quartet?
Baker on trumpet, Bob Whitlock on bass and Chico Hamilton on drums (later Mulligan himself would occasionally double on piano.

Question: Did the make any recordings?
Self-contained rewrite: Did Gerry Mulligan and Chet Baker's quartet make any recordings?