Preheat oven to 400 degrees F.
Defrost the puff pastry in the refrigerator overnight or for 3-4 hours, or by the method recommended by the manufacturer.
With a sharp knife, cut a circle around the top rim of the brie, about 1/8 of an inch from the edge, cutting just through the rind.
Using a spoon, scoop off the rind. Set aside brie.
On a lightly floured surface, roll out pastry gently until it is a 13” x 13” square.
Place dough on a parchment or Silpat lined sheet pan.
Place the brie in the center of the dough.
Spoon the chutney onto the top of the brie.
Bring the corners of the pastry together above the brie (an extra set of hands are helpful here).
Pinch the dough together at the top of the Brie, and then tie with a piece of cooking twine. Allow the loose ends (the four corners of the dough square) to fold down so the pastry looks like a tied pouch or package.
Whisk 2 tablespoons of water with the egg and brush over the pastry, chill for 15-30 minutes.
After chilling, place the brie into the oven and bake until golden brown, about 30-35 minutes.
Serve with sliced apples, baguette rounds and/or crackers.