Preheat your oven to 400°F (200°C).
Line a baking sheet with parchment paper.
In a mixing bowl, combine the shredded chicken, cream cheese, mozzarella, Parmesan, and mayonnaise.
Season with garlic powder, onion powder, salt, and pepper. Mix until everything is evenly incorporated.
On a lightly floured surface, roll out the puff pastry sheet into a rectangle (if needed). Transfer the pastry to the prepared baking sheet.
Spoon the chicken mixture lengthwise down the center third of the puff pastry. Using a sharp knife, cut 1-inch wide strips on both sides of the filling, leaving the center intact.
Fold the strips over the filling, alternating sides to create a braided pattern.
Brush the entire braid with the beaten egg for a golden finish. Bake in the preheated oven for 20-25 minutes, or until the puff pastry is golden brown and fully cooked.
Let the braid cool slightly before slicing. Serve with a fresh salad, roasted vegetables, or your favorite dipping sauce.