Using a meat mallet, or rolling pin, pound out the chicken breasts until each one is 1/4 inch in thickness. This allows the chicken to cook quickly and evenly. Sprinkle both sides with salt and pepper and then set aside.
In a medium bowl, mix together the sour cream and 2 tablespoons of the ranch seasoning packet.
Place the chicken breasts into the sour cream mixture and, using tongs or your hands, mix together until the chicken is completely coated.
Cover and let the chicken marinate for at least an hour. If you can prepare this step in the morning or the night before, to marinate longer, then even better.
Preheat the oven to 425 degrees.
In a medium bowl, mix together the rest of the ranch dressing mix, panko breadcrumbs, parmesan cheese, and shredded cheddar cheese.
Dip the marinated chicken breasts into the panko mixture and place on a sheet pan, or in a baking dish, coated with olive oil.
Divide the remaining panko mixture between the chicken breasts.
Bake for 25 - 30 minutes or until the chicken is cooked through. The internal temperature of the chicken should be 165 degrees when it's cooked completely.
Serve with a salad, rice, or vegetables.