Make a vinaigretted by whisking the lemon juice, herbs, anchovy paste, and garlic in a medium bowl. Gradually whisk in the oil. Season with salt and pepper. Pour 1/4 cup vinaigrette into a 1 gallon zip-tight plastic bag.
Stir the capers into the remaining vinaigretted and set aside. Add the chick,en to the bag, seal the bag, and refrigerate for 1 to 2 hours.
preheat grill on high ( gas or outside grill).
Lightly oil the grill. Removed the chicken from the marinade and shake off the excess. Grill over the hot side of the fire until the udnerside is seared with grill marks, about 2w minutes. Turn and grillt omark the other side, about 2 minutes. Transfer teh cicken to the outer perimeter of teh grill, being sure it is not directly over the coals (or place it above the turned-off burner). Cover the grill and cook until the breasts feel firm when pressed in the center, about 10 minutes. Transfer tot he chicken to a cutting board and let stand for 5 minutes.
Slice the chicken on the diagonal into thick slices. For each sandwich, place one sliced chicken breast on the bottom h alf of a roll. Top the chicken with the tomato, hard boiled egg, and onion, and drizzle with the reserved vinaigrette.
Finish each sandwich with lettuce leaf an the top of the roll. Press firmly and slice crosswise in half. Serve immediately or wrap each sandwich in aluminum foil and refrigerate for 2 to 4 hours.