Preheat a gas grill to medium-high (400-450°F). (Or, for a charcoal grill, build a fire with coals in the bottom center of the grill and let it burn down to medium-high heat, about 400-450°F.)
Toss asparagus, mini peppers, zucchini, oil, garlic, salt and pepper in a large bowl until evenly coated. Divide the mixture evenly among 6 sheets of foil. Working with 1 foil sheet at a time, bring up 2 sides of the foil to meet in the center. Create a tight ½-inch fold to seal. Fold over 1 more time, making sure to leave space in the packet between the vegetables and the foil. Fold the other sides of the foil in, creating a sealed foil rectangle.
Place the foil packets, sealed-side up, on the grill rack; grill, covered, for 4 minutes. Flip the packets; grill until the vegetables are tender, about 4 minutes more. Remove from the grill.
Stir butter, parsley and chives together in a small bowl. Carefully open the foil packets. Place 1 teaspoon butter mixture in each packet; reseal the packets and let stand until the butter melts, about 1 minute.
