1 and 1/2 pounds baby new red potatoes, halved or quartered if large
1 tablespoon plus 1 and 1/2 teaspoon olive oil
3 garlic cloves, minced
2 tablespoons white-wine vinegar
1 and 1/2 tablespoons fresh thyme leaves, chopped
1 and 1/2 pounds chicken cutlets
1 and 1/2 pounds asparagus, trimmed
1 tablespoon butter
Heat a grill to medium. Fold a 4-foot-long sheet of aluminum foil in half to make a double-layer sheet. Place the potatoes on the double layer. Form a packet, folding the foil over the potatoes and crimping the edges to seal. Place on the grill and cook, turning over once, until the potatoes are tender, about 25 minutes. Remove from the heat. Leave the potatoes wrapped in foil to keep them warm. Raise the grill to high; lightly oil the grates.
While the potatoes are cooking, make the marinade: In a large baking dish, whisk together 1 tablespoon of the oil, the garlic, vinegar, tyme, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add the chicken; turn several times to coat. Let marinate at room temperature for 10 minutes.
In another dish toss the asparagus with remaining 1 and 1/2 teaspoons oil; season with salt and pepper.
Lift the chicken from the marinade and grill until browned and cooked through, 2 to 3 minutes per side. Grill asparagus, turning occasionally, until lightly browned and tender, 4 to 8 minutes, depending on the thickness of the spears.
Remove the potatoes from the foil; transfer to a medium bowl, toss with the butter, and season with salt and pepper. Cut the asparagus on the diagonal into 1 and 1/2-inch pieces. Serve the chicken with the potatoes and asparagus.