Stir together vinegar, onion salt, pepper, rosemary, thyme, and onion. Slowly add oil, whisking to blend. Put marinade and chicken pieces in a large, zippered plastic bag and refrigerate 30 minutes to 12 hours, turning occasionally.
Preheat grill. Cook chicken pieces over medium, indirect heat for 30 to 40 minutes or until juices run clear. Breasts are done when juices run clear and a meat thermometer inserted in thickest part registers 170° F. Thighs and drumsticks are done when juices run clear and a meat thermometer inserted in thickest part of thigh registers 180° F.