Pound the chicken breasts until they're even and thin enough that they could be rolled up. Mix the goat cheese, garlic, and oregano in a small bowl.
Place one slice prosciutto atop a chicken breast. Spoon 1/4 of the goat cheese mixture on top of the prosciutto. Roll the chicken up and secure it with toothpicks. Repeat with remaining breasts, and then brush each piece of chicken with olive oil.
Preheat your grill. When ready, grill the chicken for eight to 10 minutes or until the chicken is cooked through.