In a large bowl, combine all ingredients EXCEPT chicken and zucchini (oil through broth). Whisk together. Place chicken in a large zipper topped plastic bag, pour mixture all over the top of the chicken, make sure chicken is fully saturated, let out excess air, seal and place in refrigerator to marinate for at least 2 to 3 hours or overnight.

At time of cooking, preheat grill pan or skillet to medium-high heat.

Remove chicken from fridge and marinade. Grill for about 4 to 6 minutes per side, or until chicken is cooked through. Brush zucchini halves with olive oil, season lightly with salt and pepper, and grill for about 2 to 3 minutes per side or until tender. Serve with drumsticks.