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.
Did the make any recordings?
Mulligan's first recording sessions in Los Angeles were produced by Bock for Pacific Jazz.

Question: What was the name of the first album they recorded?
Self-contained rewrite: What was the name of the first album Gerry Mulligan and Chet Baker's quartet recorded?