Before leaping to firing that person, you'd want to talk to them and explain that the misbehaviour has to stop. There may be personal reasons, and the person may need support to change. But if the behaviour doesn't shift then yes, dismissal is absolutely appropriate. The demoralisation stemming from a misbehaver who is protected from on high can be huge.

Great performance does not require being an asshat. It's (nearly?) always possible to find an equivalent performer who's pleasant to be around and a constructive team member.