Arrange the chicken, skin side up, on the grill grates. Cover and cook until the chicken is cooked through and the skin is crisp (the internal temperature should read 165˚F), about 15-20 minutes. Brush the chicken lightly with the romesco sauce. Using tongs, flip the chicken over and brush with more sauce. Cook 2-4 minutes (uncovered), until the romesco sauce is lightly caramelized on the skin side. Flip the chicken over one more time and let it cook for a few seconds longer.