Dip the chicken into the egg and coat it, let any excess egg drip off. Place the chicken into the cracker crumb mixture and press the crumbs in on both sides. Place the chicken into the baking dish. Repeat with the remaining chicken. Take ¼ cup of the leftover cracker mixture and sprinkle it on top of the chicken. Place the diced butter around the chicken, not directly on top.
Once the ritz cracker chicken has completely cooled, transfer it into an airtight container. Leftovers can then be stored in the refrigerator for 3 to 4 days.