Dice the chicken into small cubes. Chop the broccoli florets and red bell pepper.
In a skillet over medium heat, add chicken, broccoli, and red bell pepper. Stir in the cream cheese and cheddar cheese. Mix thoroughly until the cream cheese is melted and the mixture is creamy. Season with salt and pepper to taste.
Roll out the crescent roll dough. If using crescent rolls instead of a sheet, gently press the seams together to seal.
Cut the dough into 6 equal squares. Place a heaping spoonful of the chicken mixture in the center of each square, leaving space around the edges. Bring the edges of each square up and over the filling, pinching to seal. Place the pockets seam-side down on a lightly greased baking sheet.
Bake for 15-20 minutes, or until the pockets are golden brown.