Pat the chicken dry with paper towels and trim any excess fat.

In a large ziplock bag, combine the yellow mustard, white vinegar, Worcestershire sauce, and thyme. Add the chicken, seal tightly, and massage to coat. Refrigerate for at least 4 hours or up to 24 hours.

Set a small saucepan in your sink and drain the chicken through a colander over it to catch all the marinade. Set the marinade aside and do not discard it.

Preheat your grill to high heat. For a gas grill, turn all burners to high. For charcoal, build coals on one side only to create a direct and indirect heat zone.

Place the chicken skin side down over direct heat, close the lid, and sear for 3 to 5 minutes until deeply golden and pulling away from the grates cleanly.

Flip the chicken and move it to the indirect side of the grill. Turn off the burner directly underneath and reduce remaining burners to medium-low, targeting 250 to 275 degrees F. Close the lid and cook for 15 to 30 minutes until internal temperature reaches 165 degrees F.

While the chicken finishes cooking, add the molasses to the saucepan with the reserved marinade. Bring to a boil over medium heat, then reduce to low and simmer gently until ready to serve.

Remove chicken from the grill, rest for 5 minutes, then serve with the warm mustard molasses sauce on the side.