Cut chicken breasts into similarly-sized pieces for the skewers. Place in an airtight container or zip-top bag and set aside.
Whisk together all of the marinade ingredients.
Pour marinade into the container with the chicken. Seal the container and transfer to the refrigerator. Marinate at least one hour.
Preheat the grill to medium-high heat.
While the grill is preheating, cut the pepper and onion into skewer-sized pieces.
Assemble the skewers with alternating pieces of chicken, pepper, and onion.
Coat the grill grates in high-heat cooking spray.
Grill the skewers on direct heat for about 10 minutes, turning every few minutes so they don't burn.
Transfer the skewers to indirect heat and cook for about another 5 minutes until the chicken is cooked through and the juices run clear. (Note: Depending on your particular grill and how big you cut the chicken pieces, they may need more cooking time.)
If you are using wooden skewers, soak them in water for at least 15 minutes so they don't catch on fire.