Start your Grill on 'smoke' with the lid open until a fire is established in the burn pot (3-7 minutes). Preheat to 350F.
Blend butter, chives, minced garlic, and black pepper in a small bowl. Cover with plastic wrap and set aside.
Butterfly the tails down the middle of the softer underside of the shell. Don't cut entirely through the centre of the meat. Brush the tails with olive oil and season with salt, to your liking.
Grill lobsters cut side down about 5 minutes until the shells are bright red in color. Flip the tails over and top with a generous tablespoon of herbed butter. Grill for another 4 minutes, or until the lobster meat is an opaque white color.
Remove from the and serve with more herb butter and lemon wedges.