Pat the chicken dry with paper towels, then place breast side up in a large cast iron or 2 quart casserole dish.
In a small bowl, combine the butter, thyme, salt, and pepper. Once fully mixed, rub the butter mixture evenly over the chicken, then tie the legs together with kitchen twine.
Add the cherries, chicken broth, and balsamic vinegar around the chicken, then nestle the thyme sprigs into the cherries.
Bake for 1 hour and 15 minutes to 1 hour and 30 minutes, until the legs pull away easily and a thermometer inserted into the thickest part of the breast registers 165 F.
Let rest for at least 10 minutes, then carve and serve alongside the cherries!
Notes
*substitute with coconut oil or EVOO for Whole 30 compliance