In a blender or food processor, combine the lime juice, olive oil, tamari, chili pepper, garlic, paprika, cuming, coriander, oregano, salt, and pepper. Blend to a coarse puree.
Adjust seasonings to taste, and add a little hot sauce if desired.
Place the chicken in a single layer in a large dish and pour the sauce overtop. Turn the chicken a few times to coat. Let marinate for at least 1 hour and up to 4 hours.
Set up your grill for indirect heat on one side. Place the chicken thighs, skin-side down, directly over the heat first. Let cook, watching carefully for flares, until the skin is nicely browned and has grill marks, 4 to 5 minutes.
Flip the thighs and grill over direct heat for another 4 to 5 minutes, then move to indirect heat until the thighs register at least 165ºF on an instant read thermometer.
Creamy Cilantro Sauce (optional)
Add all ingredients to a blender and blend until smooth. Adjust seasonings to taste.
Drizzle over the chicken at the table.
Preheat the oven to 400ºF and cook the chicken, skin side up, for 35 to 40 minutes. The internal temperature should reach 165ºF on an instant read thermometer.
Store any leftovers in the fridge in a covered container for up to 5 days.