Preheat the oven to 350°F.
In a mixing bowl, combine the shredded chicken, cream cheese, cheddar cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Unroll the crescent roll dough and separate it into triangles. Place a generous spoonful of the chicken mixture at the wide end of each triangle.
Roll the dough around the filling, starting from the wide end and rolling towards the point. Pinch the edges to seal.
Dip each chicken pillow in melted butter, then roll in crushed Ritz crackers to coat.
Place the chicken pillows on a baking sheet lined with parchment paper. Bake for 20-25 minutes or until golden brown.
Let cool for a few minutes before serving.