The general consensus on Chaos Eldar is that if they exist at all they're very, very rare. Due to the nature of her birth, Slaanesh owns the soul of every single Eldar upon birth.
This is why I think you'd have to come up with a really solid fluff reason for a Slaaneshi, Khornate or Nurglite chaos eldar force. Anything goes in
40k, so for it to be fluffy you'd just need a good explanation.
I don't think 'dedicating yourself to Khorne or Nurgle' in realspace would be enough to sever the connection their soul has to Slaanesh, although you shouldn't really let that stop you from making them unless you're a fluff-
wh*re like me

.
However, taking some inspiration from the fluff where a force of Eldar Farseers travel into the warp and into Nurgle's garden in search of Isha. They get all the way to where Isha is kept, where Nurgle turns them into petrified trees in the shape of themselves.
What if, in the heart of the realm of another chaos god, Slaanesh holds no power. At the point of these Eldar's death, their connection with Slaanesh is severed. There's nothing stopping Nurgle bringing these petrified Eldar back to life in horrific diseased forms for his own amusement. They're his playthings now.
That's what the idea for my Croneworld Eldar is actually. Again, they're a bit contentious, but it's too good of an opportunity to pass up.
My idea is that the Eldar didn't fall just by themselves. They were pushed.
We know so little about that time that it's possible that the events as we know them aren't the whole story.
Basically, I'm thinking that Slaanesh had followers even before she was born. The eldar goddess Lileath prophesised that the eldar race would destroy Khaine, who when he heard it went on a murderous rampage killing a lot of eldar before Asuryan stopped him.
My thinking is that the eldar both respected Khaine for his strength, and resented him for this slaughter. When some of their most powerful psykers felt the gestation of a new eldar god in the warp, they thought that this was the prophesy come true.
A new eldar god of peace-time that would forever free them from the spectre of war.
Oh how they were mistaken.
In the present day, these pleasure cults dedicated to Slaanesh can be found still, cavorting on the Crone Worlds in the heart of the eye of terror. I'm purposefully leaving it ambiguous as to whether they're still living eldar from the fall, or apparitions created by Slaanesh.
Either way, when I get round to making them I'll use the chaos daemons codex to represent them as daemonette's high
WS and I, plus S/T3 fits an eldar profile nicely