Mix chili sauce, vinegar, horseradish, garlic and salt in a bowl. Reserve 1/2 of the marinade. Add chicken to bowl; turn to coat. Cover; marinate in refrigerator for about 5 minutes.
Preheat grill or broiler. Remove chicken from marinade; discard marinade in bowl. Place chicken on grill or on broiler pan. Grill or broil chicken, turning and basting frequently with half the reserved marinade, until juices run clear when a meat is pierced with a knife, about 30 minutes.
Heat remaining reserved marinade in a small saucepan, stirring occasionally. Serve hot alongside chicken.