1. In a medium bowl mix marinade with butter, basil, and tarragon. Add lemon juice, chives, and oil and stir until well combined. You can make the sauce several hours ahead of time; cover and refrigerate until ready to use.
2. Preheat grill until moderately hot (about 400 degrees). If using gas, turn off the burners on one side so you have direct heat on one side and indirect heat on the other. If using charcoal or wood, push it to one side, leaving the other side without any direct heat underneath. Place a grilling tray on the side of the grill without any direct heat.
3. Place a lobster on a clean work surface upside down (shell side down). If desired, place a tea towel over the lobster's head. Plunge a sharp knife into the body directly below the head and split the lobster open cutting down the middle, without separating the lobster into two distinct halves. The legs may continue to wave for a minute. Remove and discard the sac at the top of the head, if you see it. Use a lobster or nutcracker to make a small crack in each claw (this prevents them from bursting during grilling). Remove the rubber bands from the claws and discard. Place lobsters on a broiler pan.
4. Divide the sauce among the four lobsters, drizzling it over the body and the tail meat. Remove lobsters from broiler pan and place them, shell side down, on the grilling tray on the side of the grill without direct heat. Cover the grill and cook 15 minutes.
5. Remove the cover and move the lobster to the side of the grill with direct heat and cook another 4 to 6 minutes, or until the tail meat feels firm. Serve hot.
Source: Hannaford fresh Magazine, July -,- August 2012