In a bowl, combine oil, orange juice, lemons, limes, salt, pepper, and garlic cloves, saving juiced fruit. Whisk together. Place chicken, juiced pieces of fruit, and quartered onions in large plastic bags or bowl. Pour marinade over the top, tossing to combine. Cover with plastic wrap (if using bowl) and marinate for at least two hours.Overnight is best. Toss a few times during the marinating process.
Preheat broiler to high. Arrange oven rack toward bottom of oven.
Lay chicken on a broiler pan, or other baking dish with a drip tray. Broil for 25 minutes,turning once and grilling other side. Remove pan from oven when done.