Pre-heat the oven to 375 degrees F. Grease a baking pan or skillet.
Cut all of the chicken breasts in half. Taking each half, make a long slit down the middle of the chicken breast big enough to fit the cheese in. Season each one with salt and pepper.
In a shallow bowl, mix together the olive oil, garlic, and the finely chopped rosemary.
Taking each chicken breast half, dip it in the olive oil mixture making sure to coat both sides. Place the seasoned chicken in a baking pan or skillet.
Stuff each piece of chicken with ~1 tablespoon of the goat cheese. You can add more or less depending on your chicken and how much you want.
Top each piece of chicken with a sprig of rosemary and then wrap each one in a piece of prosciutto. If needed or desired, you can use a toothpick to hold the prosciutto closed.
Bake for 35-45 minutes checking for done-ness at the 35 minute point.