I have seen several questions similar to this one closed for being too broad, but it certainly seems like an often-enough asked question that I will attempt to narrow the focus down such that it is both answerable and useful.
As an online GM in the past, I have had multiple players apply for my games with Chaotic Evil characters. I never accepted them, for all of the various reasons a GM running a heroic game would be wary of Chaotic Evil, but I have recently begun taking a closer look at the alignment to see if I would be able to craft a Chaotic Evil character capable of working with a heroic party.
As far as I can tell, such a character (not just for myself) would require the following at a minimum:
- A mature player who understands that this is a team-based game
- An in-character reason to work with the party
- The capacity to grow as a character
- A strong understanding of the differences between "Chaotic Evil" and "Chaotic Stupid"
I would like to allow my players more freedom to choose their alignments in the future, but I cannot guide them through the creation and play of a Chaotic Evil character if I do not know what kinds of challenges they will face.
In your experience, what challenges would a character who fits the above qualifications but is still Chaotic Evil have integrating into a heroic party, while retaining a Chaotic Evil alignment?
To clarify the type of answer I am looking for, I am not asking about whether or not Chaotic Evil could be integrated, or if it should be, or what "Chaotic Evil" means to you. Since those are all opinion-based, please speak from your experiences playing your version of Chaotic Evil, playing alongside another person's version of Chaotic Evil, or GMing a heroic party with at least one Chaotic Evil character in it.
Also, please assume that any interpretation of what "Chaotic Evil" means is valid, assuming it is reasonably south of "Good" and "Lawful". If the game was supposed to be primarily Lawful Evil, such experiences also work just fine from this different angle. Not unappreciated and close enough to be on-topic would be specific examples of how the experience playing, playing with, or GMing for the character was good or could have been improved, but I would ask that these be helpful anecdotes or examples instead of the answer.
On the off chance your answer depends on the system your experience occurred within, please identify the system. Else, I expect most answers to be universal between Pathfinder and the various versions of Dungeons and Dragons, possibly among other games using this alignment system.