Prepare your heat source: Build a campfire and let it burn down to a bed of hot coals (medium-high heat), or preheat a gas grill to 400°F (200°C).
In a large bowl, whisk together the condensed cream of chicken soup, milk (or broth), garlic powder, dried thyme, salt, and pepper until smooth.
Add the diced chicken, potatoes, carrots, peas, and corn to the bowl. Stir well to coat all ingredients evenly with the creamy sauce.
Tear off 4 large sheets of heavy-duty aluminum foil (about 18 inches long each). If using standard foil, use double layers for each packet to prevent tearing.
Divide the chicken and vegetable mixture evenly among the center of the four foil sheets.
Top each mound of filling with the quartered biscuit dough pieces (distribute them evenly on top of the mix). Dot with butter if desired.
Fold the foil over the mixture to create a packet. Seal the top and sides tightly, but tent the top slightly (leave a little air gap) so the biscuits have room to expand without sticking to the foil immediately.
Place the foil packets on a grate over the hot coals or directly on the grill grates. Avoid placing them directly in the fire to prevent burning the bottom.
Cook for 30-40 minutes, rotating the packets halfway through. The packets are done when the potatoes are tender and the chicken is fully cooked (internal temp 165°F).
Carefully open a packet (watch out for hot steam) to check doneness. Let them cool for a few minutes before serving.