In a large bowl, whisk together the yogurt, vinegar, curry powder, garlic, and salt. Add the chicken and toss to coat. Cover and marinate in the fridge for 12 to 24 hours.
If you are using wooden skewers, place them in a container with water to cover for 30 minutes. Preheat the grill to medium-high.
Thread the chicken on the skewers, placing the pieces close to each other but not touching.
Grill, covered, for 6 to 8 minutes total for white breast meat, 8 to 10 minutes for thighs, turning the kebabs about every 2 minutes so that the chicken has nice grill marks on most of the sides and is cooked through.
Transfer the skewers to a serving platter and sprinkle with the chopped mint, if using. Serve over basmati rice with mango chutney, if desired.
Notes
Make sure there isn’t too much marinade on the chicken pieces, though definitely don’t scrape too much of it off. The more full-fat the yogurt, the thicker the marinade will be.
Thread the chicken on the skewers, placing the pieces close to each other, but not touching so they brown on all sides and cook faster.