Prepare a hot grill fire.
Put one chicken breast on one side of a large piece of plastic wrap. Drizzle about 1 tsp. oil on the breast and loosely fold half of the plastic wrap over the chicken. (There should be enough room to allow the chicken to expand when you pound it.) Using a meat mallet or a heavy sauté pan, pound the chicken so that it’s about 1/2 inch thick. Discard the plastic wrap and repeat the process with the remaining breasts. Season the chicken with salt and pepper on both sides, and coat with 2 Tbs. of the oil. Let sit at room temperature while you prepare the other ingredients.
In a medium bowl, combine the olives, almonds, capers, parsley, lemon zest, thyme, garlic, and 1/2 cup of the oil.
Lay the chicken on the grill and cook, undisturbed, until it has grill marks, 2 to 3 min. Flip the chicken and continue to grill until it’s cooked through, about 2 to 3 min. more. Transfer to a clean cutting board. Let rest for 2 to 3 min. Holding your knife at an angle, cut the chicken into 1/2-inch-thick slices and arrange them on a platter or on four dinner plates. Spoon the relish on top or to the side of the chicken and serve immediately.