Chuckles was an accomplice of The Joker in the robbing of Gotham National Bank.
When they are being briefed on the heist on the way to the bank, Chuckles points out to Grumpy that they have to split it into six shares instead of five, pointing out that the person who planned the heist also counts; he is accosted by Grumpy who implies that he doesn't deserve a share for "sitting out".
Along with Grumpy and "Bozo" (actually the Joker in disguise), he was one of three thugs to take over the bank's lobby. He had just knocked out a security guard with his gun and was ordering people to stay down when he was shot in the back and killed by the Manager of Gotham National Bank. It is unknown if he had a double-cross method or not, as he was killed before the double-crosses began.
A clown named Chuckles appeared on The Mary Tyler Moore Show. He may have taken his callsign from this fictional clown. Similar to the bank robber, his namesake was also killed unexpectedly. In that case, however, it was from an rogue elephant during a Circus parade, of which he was the grand marshall.