Preheat the oven to 425 degrees F. Prepare the chicken by pounding thin using a mallet or rolling pin in a resealable freezer bag or between pieces of wax paper (about 1/2 inch in thickness). Salt and pepper both sides of each chicken breast and set aside.
In a small bowl mix together the goat cheese, dried figs, pecans, thyme, and minced garlic. Continue to mix until evenly combined and the goat cheese is a little softened.
Prepare each chicken breast by spooning the the goat cheese fig mixture evenly divided among each chicken breast, and fold the breast in half. Now wrap the prosciutto around each breast, using 3-4 slices per breast covering the entire chicken. This helps to also secure the filling in place! Place inside a casserole dish.
Transfer to the oven, and bake for 15 minutes at 425. Bump up the temperature to 450, and bake an additional 5-10 minutes (depending on size of chicken) until the internal temperature reaches 165 degrees. The prosciutto will be slightly crispy.
Remove from oven and let rest for 5 minutes before serving. Spoon any of the juice remaining in the pan on top of each chicken. Garnish with thyme to serve!
*For an added elegance to this dish, take the juices from the pan, and pour into a medium saucepan with 1 cup white wine. Add in 1 tbsp arrowroot starch to thicken. Bring to a boil, reduce the heat to a simmer for 3-4 minutes. Pour on top of each chicken.