Gather the ingredients. Preheat an outdoor grill for medium-high heat.
Stir vegetable oil, cider vinegar, garlic powder, black pepper, salt, basil, and thyme together in a bowl; set aside.
Lay out four 12x12-inch squares of aluminum foil. Place 1 chicken breast in the center of each square, top with potatoes, onions, bell peppers, and mushrooms. Ladle 1/4 of the sauce on each and fold the foil around the ingredients to form four sealed packets.
Grill the packets on the preheated grill until chicken is cooked through and tender, about 30 to 40 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
