Place trimmed chicken breast in a large, Ziploc, plastic bag. Pound with a meat pounder or a rolling pin until ¼ inch thick. Repeat with all chicken breasts, each breast should be about 8 inches long and 6 inches wide.
Lay the chicken breasts smooth side down on work surface and season with salt and pepper. Spread evenly about 2 tablespoons hummus on the chicken breasts leaving about ½ inch border all around. Roll each chicken breast and wrap each rolled breast in a sheet of aluminum foil (or plastic wrap works also). Twist the ends like a candy wrapper and chill in the refrigerator about 45 minutes.
Heat oven to 400° degrees. Using 3 pie plates (or shallow dishes) pour the flour in one, lightly whisk the egg whites and water in the other and place the breadcrumbs in the other. Unwrap the chicken breasts and using tongs, roll in the flour (shake off excess), then submerge in the egg whites (let the excess drip off) and then finally place in the breadcrumbs, use your fingers to press the breadcrumbs so that they stick.
Heat 1/4-cup olive oil in a large non-stick skillet until shimmering, about 4 minutes. Place the rolled chicken breasts in the oil, seam side down. Cook until golden, about 2 minutes on all sides. Put the chicken breasts (seam side down) in a baking dish and cook about 15 minutes or until thermometer registers 160 degrees. Remove from oven and let sit for 5 minutes. Using a sharp knife, slice on a bias into 4 or 5 pieces. I like to serve this dish with a side of vegetables, such as sautéed Spinach or a side of rice for a more filling meal.