In a medium bowl, combine yogurt, lemon juice, olive oil, tomato paste, paprika, cayenne, allspice, and black pepper.
Using a mortar and pestle, crush garlic cloves with the salt. Add to the marinade.
Cut chicken into 1"-2" pieces. Coat with the marinade and refrigerate 1-4 hours.
Pierce the chicken onto the skewers, wiping off any excess marinade. Grill until the chicken is cooked through, about 10 minutes, turning after 5 minutes.
Serve with flatbread, vegetables, and garlic mayonnaise (toum).