Trim any excess fat from chicken thighs and place them in a zippered plastic bag.
Combine all dried spices in a small bowl. Combine olive oil, lime juice and vinegar in a measuring cup, and stir in spice mixture.
Pour mixture over chicken in bag, zip closed and work the marinade around the chicken pieces to coat them all. Marinate in fridge for at least an hour and up to 8 hours, turning bag a time or two to redistribute the marinade.
About 1/2 hour before you’re ready to grill the chicken, remove it from the fridge to bring it at least partially to room temperature.
Prepare grill for indirect grilling, with the coals to one side. When the coals are good and hot, remove chicken from marinade, shaking off excess. Discard marinade in bag. Start the chicken on the side away from the coals, skin side down. Cook for 3 to 4 minutes, then turn and cook skin side up for 2 to 3 minutes.
Move the chicken thighs directly over the coal, skin side down, and close grill (peek through the vents to see if there are any flare-ups—if so, partially close vents to make them subside). Cook for about 2 minutes, then turn and cook skin side up for another 2 minutes, again watching for flare-ups.
Start checking the temperature on the chicken with an instant read thermometer. The chicken is done when it’s at least 165ºF in the thickest part. If some pieces cook faster than others—and they inevitably will—move done pieces to the indirect heat side of the grill or transfer to a platter and tent with foil.
When all chicken is done, let it rest for 5 minutes, then serve. And honestly, if it comes to room temperature as you finish preparing other parts of the meal, that’s totally fine.