Cook pasta according to package directions, omitting salt and fat.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Sprinkle chicken with salt and pepper. Add chicken and asparagus to pan; sauté 5 minutes. Add tomatoes and garlic to pan; sauté 1 minute. Remove from heat. Stir in pasta, basil, vinegar, and oil. Arrange 2 cups pasta mixture on each of 4 plates; top each serving with 1 tablespoon cheese.