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Hi I'm Brian and I'll be happy to help you try to diagnose this!
There are a couple things that can do that. Which one depends on the model of your ac unit. It could be either a compressor contactor with stuck or welded contact points. Or, in the case of some of the newer ultra-high efficiency units, the unit control board actually turns the compressor on and off and the board has a failure condition. I would need the make and model number of the unit to tell which it could be. If you want to send that info, I'll try to narrow this problem down for you.
Ok thanks. That unit will not have a control board that makes and breaks power to the compressor, the compressor will be started and stopped by a compressor contactor. So, either you have a stuck contactor or (and I forgot to mention this possibility earlier), you have a short in the low voltage control circuit somewhere between your thermostat and indoor unit somewhere that is causing a signal to run to be sent to your compressor when it shouldn't be. There are rare circumstances where a thermostat cooling relay is stuck but that is a stretch, disconnecting the wire at Y on the thermostat can confirm that.