Combine orange and lemon juices, oil, garlic, cumin, paprika, salt and oregano in a resealable plastic food storage bag.
Add chicken and peppers; seal bag and turn to coat.
Place bag on a plate on the bottom shelf in refrigerator and marinate for 2 to 8 hours.
Preheat grill or grill pan.
Thread chicken and pepper halves onto 8 metal or wooden skewers, using 4 pieces of chicken and 3 pieces of pepper per skewer; coat with cooking spray. (Note: If you're using wooden skewers, soak them in water 30 minutes before use to prevent charring.).
Grill skewers, turning often, until chicken is no longer pink in the center, about 6 to 8 minutes; serve immediately.
Leftovers can be refrigerated for up to 3 days. Yields 1 skewer per serving.