In a large bowl whisk the marinade ingredients. Put the chicken breasts in the bowl and turn to coat with the marinade. Cover and refrigerate for 30 minutes to 1 hour.
In a medium bowl combine the salsa ingredients.
In a small bowl whisk the dressing ingredients. Season with 1/2 teaspoon salt and 1/2 teaspoon pepper. Pour the dressing over the salsa and toss to blend.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Lift the chicken breasts from the bowl (let some of the marinade cling to the chicken) and place on a plate. Season evenly with 1 teaspoon salt and 1/2 teaspoon pepper. Brush the cooking grates clean. Grill the chicken, smooth (skin) side down first, over direct medium heat, with the lid closed as much as possible, until the meat is firm to the touch and opaque all the way to the center, 8 to 12 minutes, turning once or twice.
Remove from the grill and let rest for 3 to 5 minutes. Cut the chicken crosswise into 1/2-inch slices.
Place two lettuce leaves on each of four plates. Arrange the chicken slices on top of the lettuce leaves. Spoon the salsa over the chicken and serve right away.