FOR CHICKEN: Pound each chicken breast between sheets of waxed paper to 7x4-inch rectangle. Place smooth side down on work surface. Rub 1/2 teaspoon olive oil and 1/2 teaspoon minced garlic over each chicken breast. Sprinkle each with 1/3 cup Fontina cheese. Top each with 3 spinach leaves, overlapping if necessary. Starting at 1 short side, tightly roll up chicken jelly roll style. Tie with string in several places. (Chicken rolls can be prepared 8 hours ahead. Cover and refrigerate.)
Preheat oven to 350F. Heat remaining 2 tablespoons oil in heavy large ovenproof skillet over medium-high heat. Season chicken rolls with salt and pepper. Add rolls to skillet and brown well on all sides, about 10 minutes. Transfer skillet to oven and bake until chicken is cooked through, about 15 minutes. Transfer chicken to plate and cool 5 minutes.
Bring sauce to simmer. Add butter 1 piece at a time, whisking just until butter melts and sauce is smooth. Spoon sauce onto plates. Cut string off chicken. Cut chicken crosswise into 1/2-inch slices. Overlap slices atop sauce and serve.