Lay out the chicken thighs and sprinkle both sides generously with salt and pepper.
Heat grill to medium. When the grill is up to temperature, lay out the chicken thighs. Grill the thighs, turning a couple of times, for 10-12 minutes, or until the internal temperature of the thickest part reaches 165°F. Transfer the grilled thighs to a platter, tent lightly with foil, and let rest until cool enough to comfortably handle. When the chicken is cool enough to handle, cut it into 1/2-inch cubes. Add them to a bowl and toss with the pesto sauce to coat evenly.
Quarter the cherry tomatoes and add them to a bowl with the sliced basil, fresh mozzarella pieces, salt and pepper to taste. Toss them together and set aside.
Lay out the lettuce leaves on a platter. Scoop some of the tomato and cheese salad onto each leaf and top with the pesto chicken. Garnish with additional thinly sliced basil, if desired. Serve immediately.