>>96850496 (OP)
It is actually easy if you break it down:
Evil as a motivation (rather than an ontological force) is coarsely defined as unrestricted selfishness, which is a problem in a cooperative game. Chaotic is defined as not following or recognizing a higher authority, therefore a "Chaotic Evil" character seems to be at odds with ever being in a party, even a party of evil characters.
You have to resolve this by choosing intrinsic motivation for the character that permits cooperation. The chaotic evil character must share some central goal with the group and base their actions around achieving that goal.
Then you extrapolate them pursuing that goal with their alignment and temperament A character that is cruel and violent may not direct his urges randomly into wanton slaughter of strangers or attacking farm animals-- he likely has more important violence to do. If he's provoked he will likely resort to force, but even then not to his own detriment unless he is also stupid on top of being evil and chaotic.
Lets in summary consider a deposed barbarian warlord as a character; exiled by his subordinates and sold into slavery across the world. His goal may be to return and exact revenge; but to do so he first seeks power and allies. If that means playing nice with others for a time, he will swallow his pride as long as he's permitted to do as he sees fit. He cares about the others in the party in so far as how they're beneficial to him, and so he won't be the one to cast the first stone over anything except interfering with his top level revenge.
The party, regardless of their alignment, will respect his brawn and efficacy and the fear he strikes into enemies. Crafty party members will plan around his violent nature and a cooperative player will find justification for him to agree when its convenient for their aims.
To wit: The player decides on the character, if the character is a problem at their conception it is because the player made them so.