In 1 1/2-quart microwavable bowl, mix chutney ingredients; cover with microwavable waxed paper. Microwave on High 5 to 8 minutes, stirring twice, until cranberries pop open. Set aside to thicken and cool.
Meanwhile, heat oven to 375°F. Lightly spray large cookie sheet with cooking spray. In 12-inch skillet, melt butter over medium heat. Sprinkle chicken breasts with pepper; add to skillet. Cook 8 to 10 minutes or until well browned on all sides. Set aside to cool slightly.
If using crescent rolls: Unroll both cans of dough; separate into 8 rectangles. Press each into 6x4-inch rectangle, firmly pressing perforations to seal. If using dough sheets: Unroll both cans of the dough; cut into 8 rectangles. Press each into 6x4-inch rectangle.
Spread cheese evenly in center of each dough rectangle; place chicken over cheese. Bring corners of dough together over chicken and press to seal; place on cookie sheet.
Bake 18 to 22 minutes or until deep golden brown, brushing lightly with egg during last 5 minutes of baking time. Stir chutney; serve with warm chicken bundles.