Arrange a rack in the middle of the oven and heat the oven to 375°F. Spread 1 1/2 cups panko into a thin, even layer on a rimmed baking sheet and bake until golden-brown, about 7 to 8 minutes. Set aside to cool while you prep the chicken.
Prep the chicken. Trim and discard any large pieces of fat from 2 pounds boneless, skinless chicken breasts. Place 1 chicken breast in a gallon-sized zip-top bag and pound with a mallet to an even 1/2-inch thickness. Set aside and repeat with the remaining breasts.
Finely grate 1 ounce Parmesan cheese (1/2 cup) and place in a wide, shallow bowl. Add the toasted panko and salt and pepper. Mix to combine. Place 1 cup Chili Lime Ranch Dressing in a second wide, shallow bowl.
Bread the chicken. Coat an oven-safe wire rack with cooking spray and fit it onto the baking sheet. Using your hands and, working with 1 piece of chicken at a time, dip in the Chili Lime Ranch Dressing so it evenly coats the chicken on all sides. Then dredge in the breadcrumb mixture, gently pressing the breadcrumbs into the chicken so they stick. Place on the rack and repeat with the remaining chicken breasts.
Bake the chicken until the breading is golden-brown and the chicken is cooked through and registers 165°F on an instant-read thermometer. About 30 to 32 minutes.