Stir together the vegetable oil, cider vinegar, garlic powder, black pepper, salt, basil, and thyme in a bowl; set aside.
Lay out 4 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 for 30 to 40 minutes, until the internal temperature of the chicken breasts reaches 170 degrees F (75 degrees C).
