Combine vinegar, soy sauce, honey, sesame oil, chile paste, and garlic, stirring until honey dissolves. Pour vinegar mixture into a zip-top plastic bag. Add chicken to bag; seal. Marinate in refrigerator 1 hour, turning occasionally. Remove chicken from bag, reserving marinade.
Preheat oven to 425°.
Place reserved marinade in a small saucepan over medium-high heat; bring to a boil. Cook for 2 minutes or until syrupy, stirring occasionally. Place chicken on a rack coated with cooking spray, and place rack in a roasting pan.
Baste chicken with reserved marinade; sprinkle evenly with salt. Bake at 425° for 10 minutes; baste. Bake an additional 10 minutes; baste. Discard remaining marinade. Bake an additional 10 minutes or until done. Let stand 5 minutes before serving.