Heat grill to medium. Fold two 4-foot-long sheets of aluminum foil in half to make two separate double-layer sheets. Place half the potatoes on each double layer. Form two packets, folding foil over potatoes and crimping edges to seal. Place on grill and cook, turning over once, until potatoes are tender, about 25 minutes. Remove from heat. Leave potatoes from one packet wrapped in foil to keep warm. Open second packet to let potatoes cool; reserve for Potato Salad. Raise grill to high; lightly oil grates.
Meanwhile, make marinade: In a large baking dish, whisk together oil, garlic, vinegar, thyme, 1 teaspoon salt, and 1/2 teaspoon pepper. Add chicken; turn several times to coat. Let marinate at room temperature 10 minutes and up to 30 minutes.
Lift chicken from marinade and grill until browned and cooked through, 2 to 3 minutes per side. Remove from grill. Cover half of chicken with foil to keep warm. Reserve other half for Grilled Chicken Cobb Salad.
Remove warm potatoes from foil; transfer to a medium bowl, toss with butter, and season with salt and pepper. In a medium bowl, toss asparagus with Vinaigrette. Serve the grilled chicken with potatoes and asparagus. Garnish with thyme sprigs, if desired.