Cut each chicken breast half into 8 pieces. Combine chicken pieces and 1/3 cup buttermilk in a heavy-duty zip-top plastic bag; seal bag, and marinate in refrigerator 30 minutes.
Preheat oven to 425°.
To prepare dip, combine mayonnaise and next 6 ingredients in a small bowl.
Remove chicken from bag; discard marinade. Insert a wooden pick into each chicken piece. Dredge chicken in breadcrumbs. Place on a baking sheet coated with cooking spray. Coat breaded chicken with cooking spray. Bake at 425° for 10 minutes. Serve warm with dip.