Preheat oven to 375 degrees Fahrenheit and line a large baking sheet with parchment paper.
In a small bowl, whisk together melted butter, minced garlic, parsley, oregano, salt, and pepper.
Roll the dough into a 10 by 15 inch rectangle on the prepared baking sheet.
Brush 2 tablespoons of the garlic butter mixture down the center third of the dough.
Spread the shredded chicken over the buttered section, then top with shredded mozzarella and grated parmesan.
Using a knife or kitchen shears, cut 1-inch wide strips at a slight downward angle along both sides of the filling.
Fold the strips over the filling, alternating sides to create a braided appearance.
Brush the top of the braided dough with the beaten egg wash.
Bake for 20 to 25 minutes or until the crust is golden brown and the internal temperature of the bread reaches 190 degrees Fahrenheit.
Remove from the oven and immediately brush with the remaining garlic butter mixture before slicing and serving.