Bring a stockpot of water to a boil. Add the lobsters head first, cover and cook over high heat for 9 minutes. Using tongs, transfer the lobsters to a large bowl; let cool. Twist off the claws. Using kitchen shears, snip the underside of the tails down the center and remove the lobster tail meat in one piece. Crack the claws with a mallet and remove the meat.
Using a heavy knife, finely chop enough of the legs and shells to make 4 packed cups. In a medium saucepan, combine the olive oil with the chopped legs and shells and bring to a simmer over low heat. Cook, stirring occasionally, for 30 minutes. Strain the oil and let cool. Whisk the vinegar into the oil; season the vinaigrette with salt and pepper.
Slice each lobster tail crosswise into 8 pieces. In a medium bowl, combine the tail and claw meat with the vinaigrette and toss to coat. Mound the mesclun on 8 plates and arrange the lobster alongside. Drizzle the mesclun with some of the remaining vinaigrette. Sprinkle with the chives and serve.
One Serving Calories 257 kcal, Total Fat 20.8 gm, Saturated Fat 2.8 gm