Combine onion, ginger, garlic, oil, lemon juice, cumin, turmeric, cinnamon, allspice, salt and pepper in blender or small food processor. Pulse until smooth. Add yogurt; pulse to combine.
Cut 2 slashes down to bone on each thigh; pierce each drumstick 4 or 5 times with tip of knife.
Combine yogurt mixture and chicken in plastic food-storage bag; push out air; seal. Refrigerate for 4 to 24 hours. Remove chicken from bag; reserve marinade.
Prepare grill with hot coals around sides. Place drip pan in center. Position grill rack 6 inches above coals. Place chicken on rack.
Grill chicken, covered, 30 minutes until no longer pink near bone, turning over halfway during cooking; brush occasionally with marinade. Makes 6 servings.
Broil chicken 6 inches from source of heat, 20 minutes per side.