Make your sauce: Add the vinegar, ketchup, brown sugar, honey, worcestershire sauce, salt, pepper and garlic to a medium saucepan and bring to a boil over medium heat. Simmer over medium heat for about 15-20 minutes, until thick and syrupy, whisking occasionally. Set aside as you cook your chicken (this can be made in advance and refrigerated).
Preheat the grill to about 450 degrees F. Grill chicken on one side for 10 minutes, flip and brush with sauce. Cook another 10 minutes or until a meat thermometer inserted in the thickest part of the breast reads at least 165 degrees F. Brush the other side with sauce and serve with remaining sauce on the side (because you will want to!).
Notes
This recipe makes a good amount of sauce -- if you want only enough for the chicken, you can probably halve it. But once you taste it I'm sure you'll want to put it on everything!