In a small mixing bowl, whisk together butter, garlic, chives, lemon juice, and
salt; set aside.
Using kitchen shears, cut the lobster shell down the middle, stopping at the tail. Use a sharp knife to cut the meat down the center without cutting all the way through. Insert a skewer lengthwise through the tail to keep it from curling while cooking.
Brush the tails with olive oil; season with salt and pepper to taste.
Preheat a grill over medium heat. Grill lobster, cut side down, for 5 minutes, until shells are bright pinkish-red. Flip the tails, baste with garlic butter, and grill for another 4 to 5 minutes, or until the lobster meat is an opaque white color and reads 135 degrees F.
Baste with more garlic butter, sprinkle with chives and serve with lemon wedges.