Heat an outdoor grill to about 425°F with a cooler indirect area and clean the grate. Pat chops dry, rub with 2 teaspoons oil and season with salt and pepper.
Brush peach cut surfaces with remaining oil. Whisk balsamic vinegar, honey and thyme in a small bowl.
Grill pork for 5 to 7 minutes per side until browned and at least 145°F in the thickest center. While the pork cooks, grill peaches cut-side down for 3 to 4 minutes, then turn and warm for 1 to 2 minutes until just tender.
Rest pork for at least 3 minutes. Cut grilled peach halves into broad wedges and toss gently with the balsamic mixture.
Serve chops with the warm peaches and a small spoonful of their dressing alongside.