Place berries in a medium saucepan and add honey, vinegar, chile powder, and dried thyme. Stir and place over medium heat. Bring to a boil and reduce heat to a gentle boil; cook for 10 minutes, or until thick and most of the berries have popped. Set aside; it will thicken as it cools.

Pat the quail dry, and stuff each cavity with two sprigs thyme. (I wrap a pair of sprigs around my finger, then put the ring of thyme in the cavity.) Brush both sides of the quail with olive oil then season well with salt and pepper. Let sit at room temperature for 10-15 minutes.

Heat grill to high. When it is ready, reduce heat to medium and oil the grates. Place the quail, breast side down on direct heat for 3 minutes, then flip and cook 3 minutes longer, or until done.

Arrange them on a platter. Stir the compote, transfer to a serving bowl, and serve on the side with the quail.