Prepare ingredients for eating. Be sure to wash vegetables and fruit before using for safety.
Purée garlic, orange juice, lime juice, sea salt, and pepper in a blender until smooth.
Put chicken pieces in a large bowl and pour purée over them, turning to coat. Marinate chicken, covered and chilled, turning occasionally, 1 hour.
Transfer chicken, letting excess marinade drip back into bowl, to paper towels, then pat dry. Reserve marinade.
Heat oil and butter in 6- to 7-quart pot over moderately high heat until foam subsides, then brown chicken in 2 or 3 batches without crowding, turning occasionally, about 6 minutes per batch. Transfer chicken as browned to a plate, reserving fat in pot.