Lightly butter 1 sheet of filo pastry. Top it with another and brush lightly with butter. Repeat the last step one more time. Cut the layered sheets into 12 squares. Place a piece of brie and small spoon of chutney into the centre of each square. Lift up corners of each square and squeeze together to form small bundles. Place each bundle on a non-stick or parchment-lined baking pan. Chill 30 minutes in the fridge. Bake 15 minutes at 375 degrees F, or until golden brown. Cool slightly, the chutney will be very hot, before serving.
Note: Bundles can be made several hours in advance, wrapped and kept stored in the fridge before baking. They can also be frozen; do not thaw before baking.