Pat chicken dry and trim any extra fat.
In a large ziplock bag, add mustard, vinegar, Worcestershire sauce, and thyme. Add the chicken, zip, and mix it up.
Refrigerate for 4 hours, or up to 24. (Or a half hour if you're in a time pinch, but you didn't hear it from me.) Drain the chicken, but do not discard the marinade.
Preheat your grill to high heat. If you are using wood or coals, make sure you leave an area of the grill with fewer coals. After the initial sear you will be cooking the chicken over indirect heat.
When it's hot, place the chicken pieces over direct heat. Close the lid and grill for 3-5 minutes, or until the outside is as crisp as you want it.
Use tongs to flip the chicken and place over the low-heat part of the grill. I have a gas grill, so I just turn off one of the burners. (The chicken should over the half of the grill that is turned off). Reduce the heat on the other half of the grill to medium-low heat, between 250-275 degrees F.
Cover and cook for 30-50 minutes, depending on the thickness of your chicken. Brush with marinade 2-3 times while cooking.
The chicken is done when it reaches an internal temperature of 165 degrees F on a meat thermometer, or you can cut it to see if the juices run clear (not pink).
If you want, you can quickly sear the other side of the chicken over direct high heat before serving.
Meanwhile, add the remaining marinade to a small pot. Add 2 tablespoons molasses. Bring to a boil, then reduce heat to low until ready to serve.
Serve the sauce with the grilled chicken. A little bit goes a long way.
I like to serve this with grilled corn, grilled peppers, watermelon, oven roasted potatoes, or a big salad.