Melt the coconut oil in a large skillet over medium heat. Add chicken, salt and pepper; cook and stir for 10 minutes or until chicken is cooked through. Allow chicken to cool, then shred into bite-sized pieces.
In a large bowl, combine shredded chicken with next 8 ingredients (avocado through onion).
Scoop a portion of chicken salad mixture onto each lettuce leaf; roll into wraps and serve immediately.