Heat a grill or grill pan to medium-high.
In a shallow baking dish, combine the yogurt, garlic, cumin, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Thread the chicken onto the 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, 1/2 teaspoon salt, and 1/4 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 individual plates and serve with the chicken.
Shortcut: Save on prep and cooking times by using packaged chicken tenders (precut strips of boneless, skinless breast meat) instead of cutting up whole breasts.