Whisk together butter, garlic, chives, lemon juice, and salt; set aside.Cut the lobster shell down the middle. Cut the meat downthe center and insert a skewer lengthwise through the tail.
Grill lobster, cut side down. Flip the tails, baste with garlic butter, and grill. Baste with more garlic butter, sprinkle with chives and serve with lemon wedges.