While Joe Chill is famously the man who pulled the trigger in the Batman comics, who killed Bruce Wayne's parents in Gotham? Like Smallville before it, Gotham centered around the origin of Batman, alongside most of his famous villains. The show opens with a young Bruce Wayne dealing with the cold-blooded murder of Thomas and Martha Wayne right in front of him, which sets him on the path to one day donning a cape to protect his city. It also followed young cop Jim Gordon as he dealt with the overflowing corruption and crime gripping Gotham itself.
While the pitch for Gotham almost sounds like it's setting the stage for a grounded, Chris Nolan-inspired take on the mythos, the show didn't take long to cut loose. It could be very goofy, with every passing season becoming increasingly campier and over the top. This was part of its charm for loyal followers and it went out with a bang in season 5, which covered the famous "No Man's Land" arc from the comics, where Gotham is sealed from the rest of the world and its villains run amok. It also ended with Bruce finally embracing his destiny and donning the Batman costume in the final episode.
In the Batman comics, Joe Chill was revealed as the killer of Bruce Wayne's parents. While the comic itself would present different reasons for this crime over the decades - from a simple mugging gone wrong to Chill being hired by the mob to perform the hit - the results were the same. Chill and Batman even teamed up in the now non-canon Batman: Year Two comic arc to take on a rival vigilante dubbed The Reaper, though Chill naturally didn't know Batman's true identity. He's not the killer in every piece of Batman media, such as the 1989 Batman movie, which controversially replaced him with a young Jack Napier, AKA The Joker.
Gotham itself took a different route, tying Batman's origin with the dark side of the city itself. An unidentified masked mugger shoots Thomas and Martha Wayne in Gotham's "Pilot," and it isn't until season two's "This Ball of Mud and Meanness" that Bruce tracked down "Matches" Malone (Michael Bowen, Breaking Bad), the hired gun who shot his parents. For the right price, Malone will kill anyone - though he at least draws the line at babies - and when Bruce Wayne confronts him with a gun, he starts calling him "son," since his actions somewhat created the new Bruce.
Matches at least shows remorse for what he did, and while he refuses to give up the people who hired him - eventually revealed to be Hugo Strange - he wants Bruce to kill him so he's finally punished for his many misdeeds. Bruce refuses but leaves his revolver behind, and Malone shoots himself instead. Gotham isn't the only appearance of Matches Malone in Batman lore. In the comics, Matches is the name of a dead criminal with some serious street cred, so Batman uses his identity for undercover jobs.