Heat oven to 400° F.
Place the pita chips and Parmesan in the bowl of a food processor. Pulse until coarsely ground. Transfer to a large bowl and stir in the parsley, if using.
In a medium bowl, beat the egg with 1 teaspoon water. Dip the chicken in the egg, letting any excess drip off, then in the pita-chip mixture, pressing gently to help it adhere. Place the chicken pieces on a parchment-lined baking sheet.
Bake until cooked through, 10 to 12 minutes.
In a small bowl, combine the sour cream and scallions and serve with the chicken for dipping.