Using a sharp knife, cut each lobster tail lengthwise through the shell into 2 pieces. Cover with plastic wrap and refrigerate until ready to grill the lobsters.

Shortly before grilling the lobsters, in a non-reactive mixing bowl combine the tomatoes, 8 tablespoons of the olive oil, lemon juice, lemon zest, tarragon, chives, salt and pepper and stir to combine.

Preheat a grill to medium-high.

Lightly brush the lobster tails on the cut side with the remaining 2 tablespoons of olive oil and season lightly with salt and pepper. Place the tails, cut side down, on the grill and cook for 3 minutes. Rotate the tails 45 degrees and cook the tails for 3 minutes longer. Rotate the tails 45 degrees again so that the tails are now cut side-up and cook until lobster is just cooked through, 1 to 3 minutes longer. During these last few minutes, spoon some of the vinaigrette over the cut tail meat so that it drizzles down into the lobster shells.

Serve the lobster tails with more of the vinaigrette drizzled over the meat.