To prepare the herb rub, add the listed ingredients to a food processor and process until a paste forms. Set aside.
To prepare the chicken, first make the rice. Add the chicken stock to a small saucepan and bring it to a simmer.
In another small saucepan, add the olive oil, onions, mushrooms, and garlic. Sauté over medium heat until the onions and mushrooms are cooked through.
Add the rice, sun-dried tomatoes, and a third of the chicken stock. Bring the rice and stock to a simmer and stir until the stock is absorbed. Add another third of stock and continue to stir until absorbed. Repeat with the remaining stock. Remove the rice from the heat and stir in the butter, Parmesan, artichokes, salt, pepper, and 2 teaspoons of the already prepared herb rub.
Spread the rice out on a cookie sheet and refrigerate. When completely cool, put the chilled rice mixture into a bowl and fold in the Fontina cheese.
Place the chicken breasts on a cutting board. Use a paring knife to make an inch-long incision in the thickest side of each breast. Then, put the knife in the incision and angle it upwards, cutting a pocket (about 2—3'' deep) into the top of the breast. Be careful not to cut completely through the flesh. (This will keep the stuffing inside the chicken breast while you grill.)
Fill each breast with 2—3 tablespoons of the rice mixture, being sure to stuff the mixture as far into the pocket as possible. Secure the opening with a toothpick. Then, rub the remaining herb mixture over the surface of each stuffed chicken breast.
Heat the grill to medium high. Place the chicken breasts directly onto the grill grates and cook for about 10 minutes on each side, or until a thermometer inserted into the center of the stuffing reaches 140°F. Remove the toothpick before serving.
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