Preheat the oven to 400° degrees.
Place the shredded chicken, cheese, peppers and chile sauce in a large bowl and mix to combine.
Roll out one sheet of the puff pastry on a cutting board dusted with a little flour until you have a 13' x 13' square.
Cut the puff pastry into 4 equal squares.
Fill each square with about ½ cup of the chicken filling.
Brush the edges of each square with egg wash. Take the 2 top corners and fold them down to meet in the middle, and then do the same with the bottom corners so that all four corners meet together in the middle. Seal the edges together well and then brush the top with egg wash.
Repeat with the other 3 squares and place on a baking sheet.
Follow the same instructions for the other sheet of puff pastry so that you have 8 hand pies total.
Bake for 25 minutes until browned on top, remove from the oven and let cool for 2-3 minutes before serving.