1Mix all ingredients except drummies and Avocado Mayonnaise in shallow dish. Add drummies; turn to coat. Cover and refrigerate 30 minutes to marinate.
2Heat oven to 375°. Line jelly roll pan, 15 1/2x10 1/2x1 inch, with aluminum foil. Spray foil with cooking spray. Remove drummies from marinade; place in pan. Brush with remaining marinade. Bake 30 to 35 minutes or until chicken is no longer pink when centers of thickest pieces are cut.
3Meanwhile, make Avocado Mayonnaise. Serve with warm drummies.
4Method for Avocado Mayonnaise: Mash avocado in small bowl. Stir in remaining ingredients until well blended. Refrigerate until serving.