On the Grill: Rub chicken breasts or thighs with olive oil, brown sugar, salt, pepper, cumin and paprika.
Cook on grill preheated to medium high heat for about 5 minutes on each side until cooked through. Time will vary based on size of chicken breasts or thighs. Adjust heat as necessary so chicken doesn't burn while it finishes cooking.
In the Slow Cooker: Add chicken, olive oil, brown sugar, salt, pepper, cumin and paprika to a slow cooker. Add ½ cup water.
Cover and cook on high for 2-3 hours or on low for 4-6 hours until chicken is cooked through.
Once chicken is cooked on either the grill or in the slow cooker, let cool for about 15 minutes. Shred with your hands or 2 forks.
Combine pulled chicken with all of the BBQ sauce and serve immediately or keep warm in a slow cooker for up to 4 hours.
Serve with buns, coleslaw and/or pickles or as desired.