Combine spices, salt and sugar in a large mixing bowl; stir in olive oil, soy sauce, and vinegar.
Cut lemon and lime in half, hand-squeeze juice over mixture.
Add hot pepper sauce and chopped onion, mix well.
Place uncooked chicken breasts in a large baking dish, cover with marinade mixture and soak for 2-4 hours.
Grill indoors or out, continuously basting with marinade until done.