Place on sheet of phyllo on your work surface. Brush with 1 tablespoon of olive oil. Lay a second sheet on top of the first, and brush with an additional tablespoon of olive oil. Place the third sheet on top. Place the brie towards the middle of one of the narrow edges of phyllo dough and roll up. Fold the ends of the phyllo under the brie, place onto a baking sheet, and brush with the remaining tablespoon of olive oil.
Bake in preheated oven until phyllo is golden, about 15 minutes. Place onto serving platter, and spoon the mango chutney over top.