In large shallow bowl, mix together orange juice, orange peel, olive oil, lime juice, ginger, garlic, hot pepper sauce and oregano. Add chicken, turning to coat. Cover and marinate in refrigerator about 3 hours or overnight.
Remove chicken from marinade and sprinkle with salt and pepper. Place on prepared grill about 6 inches from heat. (Chicken may also be broiled, if desired.) Grill, turning, about 10 minutes or until fork can be inserted in chicken with ease.