In a large shallow bowl or a resealable plastic bag, combine orange juice, orange zest, lime juice, olive oil, ginger, garlic, hot pepper sauce ,and oregano; add chicken. Cover and marinate in the refrigerator 3 hours or overnight.
When ready to cook, remove chicken from marinade. Sprinkle chicken with coarse salt and pepper and place on the grill
Turn the chicken often and don't let it burn. Breasts take about 25 minutes or until a meat thermometer registers an internal temperature of 165 degrees F. (juices will run clear when cut with the tip of a knife). Do not close the lid on the barbecue.
Remove from the grill and serve with side dish of rice or on its own