Check out Belkar, from the Order of the Stick. A chaotic evil character in a mostly-good-aligned party. See this quote:
Despite his kill-first who-cares-about-asking-questions attitude and lack of party loyalty causing the occasional problem, Belkar has proven to be generally effective as a party member [...] but, with carefully applied threats, the rest of the group have generally been able to keep the halfling under control and they consider him to be one of their own.
Note, though, that the OOTS keeping Belkar around has always been a bit of a stretch for willing suspension of disbelief, allowed mostly for narrative purposes, and often lampshaded by the characters themselves, so it might be a bit of a problem getting the rest of your party behind the idea of sheltering a psycho killer, but if you're fun and over-the-top enough, they might appreciate your dramatic value.
Another option that some might not like is getting explicit buy-in from the players, or at least some you think will be into it. Some might see it as a form of meta-gaming that takes away from the real roleplaying, but others might see it as a social contract that allows the party to play the roles they like and build the narratives they like.
Best Answer
Yes
In 5th edition D&D, they removed the alignment restrictions you may recall from previous editions. While the Dungeon Master's Guide offers some options for even evil-er paladins, it's perfectly possible for a normal paladin to be chaotic evil. I'm looking at you, Oath of Vengeance.