Heat grill or grill pan to medium-high.
In a shallow baking dish, combine the yogurt, garlic, cumin, ½ teaspoon salt, and ¼ teaspoon pepper.
Thread the chicken onto 8 skewers and set them in the yogurt marinade, turning to coat. Refrigerate at least 10 minutes or overnight.
Meanwhile, in a large bowl, combine the chickpeas, onion, celery, parsley, oil, vinegar, ½ teaspoon salt, and ¼ teaspoon pepper.
Remove the chicken from the marinade and cook on a well-oiled grill or grill pan, turning occasionally, until cooked through, about 10 minutes.
Divide the chickpea salad among plates and serve with the chicken.