I am an avid BBQ cook and compete in KCBS BBQ Competitions and also do some catering on the side. Here is a recipe for pulled chicken that goes well with pulled pork.
I use boneless/skinless chicken thighs (just because it is eaiser, but I do have a recipe for a whole chicken) Put on my sugar free rub. Put it on the grill for about 30 minutes. Take them off the grill and put into a pan with about 1/2 stick of butter for every 3lbs, and wrap the top of the pan with foil and put it back on the grill for another 30-45minutes.
Take off grill and the chicken will be super tender and moist and easy to pull apart or chop. I then add it back into the melted butter, and then add a little bit more of the sugar free rub, and add in sugar free bbq rub. Serve.
Another way to do pulled chicken but takes more work is to use a whole chicken. If you want that recipe, I can help you out with that.