1. Prepare grill to medium-high heat.
2. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place chicken on grill rack coated with cooking spray, and grill for 8 minutes on each side or until done. Let stand 10 minutes. Carve chicken off bones, and thinly slice.
3. Cook the pasta according to package directions. Drain well; keep warm.
4. Heat a large nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Add flour and garlic; cook until garlic is browned (about 2 minutes), stirring constantly. Add milk and broth, stirring with a whisk; bring to a simmer, and cook 2 minutes or until thickened. Add cheese, stirring until cheese melts. Add remaining 1/2 teaspoon salt, remaining 1/2 teaspoon pepper, and spinach; stir until spinach wilts. Add pasta and chicken; toss to combine.