Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a mixing bowl, combine the shredded chicken, cream cheese, cheddar cheese, ranch dressing, garlic powder, onion powder, salt, black pepper, and chives (if using). Mix until well combined.
Take each croissant quarter and place a spoonful of the chicken mixture in the center. Fold the croissant over the filling and pinch the edges to seal.
Place the filled croissant bites on the prepared baking sheet. Brush the tops with the beaten egg for a golden finish.
Bake in the preheated oven for 15-20 minutes, or until the croissant bites are golden brown and puffed.
Remove from the oven and let cool for a few minutes before serving.