It could also be a short in the wiring to that injector.
The injectors are supplied a constant +12v and are switched to ground via the transistor in the ECU, so if that wire has rubbed through and is touching the chassis somewhere it would constantly open the injector.
Disconnect the ECU plug and test the pins in that injector socket, if one is grounded then that's the problem and you have a short on the wire somewhere. If there's no short to ground on either pin then most likely the transistor in the ECU has failed.
With the ECU plugged in and ignition on the other pin should be at +12v, just to confirm you have the right one.