Whisk lime juice, yoghurt, tandoori mix, salt and pepper in a bowl. Pour mixture into a resealable plastic bag. Add chicken; coat with the marinade, squeeze out excess air and seal the bag. Marinate in the fridge for at least 2 hours.
Preheat an outdoor barbecue for medium-high heat and lightly oil the grate.
Remove chicken from the bag and transfer to a plate or baking dish lined with kitchen paper. Pat chicken dry with more kitchen paper.
Cook chicken on the preheated barbecue with lid open for 2 minutes. Close lid and continue to BBQ chicken for 6 minutes. Turn chicken, close lid and barbecue until well-browned and meat is no longer pink in the centre, about 6 minutes. An instant-read thermometer inserted into the thickest part of the thigh should read 82 degrees C.