Cut the chicken into pieces and remove the skin. Score the meat with a knife so the marinade can penetrate, then place the pieces in a large dish or Ziploc bag.
In a bowl, mix all the spices together. Add yogurt, olive oil, and lime juice and stir them all together until the mixture is smooth. If using red food coloring, stir it in a few drops at a time until it reaches your desired color intensity.
Pour the marinade over the chicken and use gloved hands (or seal the bag) to coat the chicken well. Refrigerate the chicken for at least 2 hours or up to 24 hours.
For Charcoal or Gas Grill (Two-Zone Method)Set up two zones: one hot side and one cooler side. Place the chicken on the cooler side. Cover them with the lid, placing the vent over the chicken, and cook them for about 25–35 minutes, turning each of them carefully a few times. For the last 5–10 minutes, move the chicken to the hot side for charring (this step is optional). Be sure to cook the chicken until the internal temperature reaches 165°F. Serve the grilled tandoori chicken with naan or basmati rice and garnish the dish with chopped cilantro and red onion slices.