Heat oil in a heavy skillet; or spray a nonstick frying pan with cooking spray. Saute chicken breasts until no longer pink, and juices run clear; set aside. Preheat oven to 375 degrees F (190 degrees C.)
Unroll 4 large crescent rolls. Layer each with 3 thin slices brie, 3 leaves spinach and 1 slice prosciutto. Place chicken breast in the center of dough. Wrap and tuck dough around chicken until completely enclosed. Place seam side down on baking sheet.
Bake in preheated oven for 10 to 15 minutes, or until golden brown.