The origins of the dispute are murky, but The Chin dispatched Anthony "Gaspipe" Caso to bomb Gotti's car outside his social club. However, Gaspipe mistook Gotti's then consigliere, Frankie DiCicco, for The Dapper Don. Gaspipe detonated the bomb when Frankie got in the car. Killed the wrong guy. Apparently Gotti and Gigante made up afterward.
As you may know, The Chin was the guy who shot Frank Costello in 1957 at Vito Genovese's behest. The shot grazed Costello, barely injuring him but convincing him to retire.