Zest and juice one grapefruit. You should end up with about 1/2 cup of juice and a couple tablespoons of zest. Remove the leaves from 2 sprigs of thyme, leave the rest whole.
Add the grapefruit juice, zest, thyme leaves, mustard, garlic, cayenne, and olive oil to a mixing bowl. Add a pinch of salt if you're feeling it. Whisk to combine.
Lay the chicken out in a wide dish with tall sides, like a 9 x 13 baking dish. Drop in the remaining thyme sprigs. Pour the marinade over the chicken and massage the thighs to coat with the mix.
Let marinate. Either cover and refrigerate for 4 to 8 hours, or cover and let rest on the counter for 1 hour.
Preheat grill to medium high, about 350 F to 400 F.
Remove chicken from the marinate and brush off any excess herbs or oil. We don't want those dripping onto the coals and causing a flair up. Sprinkle on some salt and pepper, if desired.
Cut the remaining grapefruit in half, then thinly slice one half of it. We're looking for 8 thin pieces to put on top of the chicken while cooking.
Place the chicken skin-side down on the grill. Put the larger grapefruit half on the grill as well. Cover and grill the chicken for about 7 to 8 minutes.
Flip the chicken and lay on the thin grapefruit slices. Cover and grill for another 4 to 5 minutes, or until cooked through.
Serve warm with your favorite sides.