Mix the orange juice, olive oil, garlic, achiote, cumin, salt and pepper together to make a marinade. You can save a bit of the marinade for basting the chicken while grilling.
Season the chicken pieces with the marinade and refrigerate for a couple of hours.
If using wood skewers, soak them in water while the chicken marinates. Soaking the skewers will prevent them from burning on the grill.
Slide the meat onto the skewers, you can also add bell pepper or onion slices if you want.
Grill the chicken skewers on both sides until done, depending on your grill, this should take 15-20 minutes.
Rotate and turn the skewers often, baste with the reserved marinade (not the one used on the raw chicken). You can use a thermometer to check the internal temperature of the chicken (165F for breasts and 175F for thighs).
Serve warm from the grill with ají hot sauce or other sauces.