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.
Notes
You can cut back on the amount of the garlic butter, if desired. Or you can omit the garlic butter.
Serve with your favorite grilled sides or surf and turf style with grilled steak.
Storing: Grilled lobster is best consumed immediately. If you have any leftovers, store them in an airtight container in the fridge for up to 24 hours.Freezing: Grilled lobster tail can be frozen after they have been cooked. Simply place them in a freezer-safe bag or container and store them for up to two months. When you're ready to eat, thaw overnight in the fridge and reheat.Reheating: The best way to reheat cooked lobster is to place it on a baking sheet and warm it in a preheated oven at 350F until heated through, which should only take a few minutes. You can also reheat grilled lobster tails by placing them back on the grill over low heat for a minute or two.