Wash and dry chicken legs. Place chicken legs in a non-metallic dish or resealable plastic bag. To make marinade, place marinade ingredients in a 2-cup measuring cup and stir until well combined. Pour marinade over chicken and cover or close bag. Marinate in refrigerator several hours or overnight.
To make basting sauce, place sauce ingredients in a 2-cup measuring cup and stir until well combined; set aside.
Preheat grill and lightly coat with oil or cooking spray. Drain chicken and discard marinade. Place chicken on prepared grill 4 to 6 inches from source of heat.
Cook 25 to 30 minutes, turning occasionally. Brush chicken with basting sauce and continue to grill an additional 10 to 15 minutes, basting and turning frequently until chicken is no longer pink inside. Watch closely to prevent over browning.