Sprinkle chicken with salt and pepper. Place a large nonstick skillet coated with cooking spray over medium-high heat. Add chicken; cook 5 minutes on each side or until done. Remove from skillet; cool and cut into thin slices. Set aside.
Add broth and vermouth to skillet, scraping pan to loosen browned bits. Add leek and garlic; sauté 10 minutes over medium-high heat or until tender. Stir in chicken and tomatoes; reduce heat, and simmer 5 minutes.
Combine tomato mixture, linguine, and cheese in a large bowl, and toss well. Spoon into bowls; sprinkle with basil.