Preheat the oven to 450°F with a rack in the center position. Line a large rimmed sheet pan with foil and place a metal cooling rack inside.
Season the chicken all over with the salt, pepper, and paprika. Arrange the chicken thighs skin side up on the prepared rack. Brush the egg whites all over the chicken.
Reduce the oven temperature to 425°F. Place the chicken in the oven and bake until the internal temperature reaches 165°F on an instant-read thermometer and the skin is crispy, about 30 minutes.