Drain cherries and set aside; slice brie into long, 1/2 inch strips. Coarsely chop basil.
Tenderize chicken breasts. (With a tenderizer or between 2 pieces of plastic wrap with a can or bottle:) Place all five breasts on a greased or parchment-lined pan. Salt and pepper each side heavily with salt and pepper. Make a slit in the center of the breast, lenghwise, making sure to not cut all the way through.
Place one slice of brie in each chicken breast, along with 6-10 cherries (depending on the size of the breast), and fresh basil. Leave 2 Tbsp. basil for garnishing on top.
Sprinkle breasts with basil. Bake chicken for 30-35 minutes. (If chicken is really thick, you may need to bake it 10 minutes longer).