In a blender, combine the orange juice, orange peel, olive oil, lime juice, ginger, garlic, hot pepper sauce and oregano. Blend into a marinade.
Place chicken breasts in a nonporous glass dish or bowl. Pour marinade over chicken, cover dish or bowl and refrigerate to marinate for at least 2 hours, or up to 24 hours.
Preheat oven to broil OR preheat grill to medium high heat and lightly oil grate.
Remove chicken from marinade (disposing of any leftover marinade) and grill or broil 6 inches from the heat source for about 7 minutes per side, or until chicken is cooked through and no longer pink inside.