To create marinade for chicken, in medium bowl mix 4 tablespoons lime juice, olive oil, cumin, red pepper, salt and pepper. In large ziplock add marinade mix and chicken breast pieces. Seal and shake to evenly coat chicken.
Marinate for 30 minutes. Do not marinate longer as the acid from the limes will start cooking the chicken.
Meanwhile, in medium bowl combine 2 tablespoons lime juice, lime zest, peanut butter, milk and sesame oil. Mix together to create dipping sauce.
Heat gas or charcoal barbecue to medium heat.
Place marinated chicken pieces on skewers, discard marinade. Pieces should be just touching each other and not packed together tightly. This allows for even cooking.
Coat paper towel with olive oil and use to lightly coat heated grill (this prevents the chicken from sticking). Place skewers on grill and cook chicken 10-15 minutes, rotating every few minutes, or until brown on outside and cooked white on the inside.
Serve chicken skewers with dipping sauce on side.
Notes
Add more or less milk to create desired thickness of sauce. Should be thick enough to stick to chicken while dipping.