Joe Chill was a hitman working for Carmine Falcone and his associates. In this continuity, he was hired by Mayor Hamilton Hill to assassinate Thomas and Martha Wayne.
Backstory
Joseph Chilton, better known as his street-name "Joe Chill" was a hitman for hire, often working for Carmine Falcone. Often hired for small time jobs, he would often murder people that either tried to double cross Falcone or threats to the organization. Joe would also be hired by a couple of Falcone's associates, include Hamilton Hill and possibly Thomas Wayne.
Eventually, Hill contacted Chill and gave him a job: Kill Thomas and his wife Martha and to make it look like a mugging gone wrong. Joe agreed and ambushed the couple as they returned from the Monarch Theater with their son Bruce. Though Thomas pleaded with him to let him and his family go, he commented that "it [wasn't] personal", before shooting Thomas in the torso and head. He then shot Martha, stealing her pearls whist she bled to death from her injuries. As Joe turned his gun to kill Bruce, he heard sirens and decided to leave, sparing the child of a similar fate.
Eventually, either due to evidence linking him to the murder or being caught whilst fleeing, Chill was arrested and sent to Blackgate Prison. His charges may have included other assassinations he carried out for Falcone and Hill. Whilst in prison, he was at attacked and stabbed to death by another prisoner or a guard on either Falcone or Hill's payroll.
Legacy
Joe's murder of Thomas and Martha would lead their son Bruce to become the vigilante Batman. It would also lead to many of Gotham's great families to "flock" together, believing that their fate could have happened to them. Bruce later found out about the connections between Chill, Falcone and Hill after news of his parents' involvement with the city's corrupt was uncovered. When later investigating Crime Alley and recounting his parents' murder, Bruce considered what he would have done if he had the chance to meet Joe Chill again, choosing between arresting him, murdering him or demanding to know why he had killed them.