Heat a large nonstick skillet over high heat. Season the chicken with the dried basil, 1/4 teaspoon of salt, and black pepper to taste. Spray the skillet with oil and add the chicken. Cook until the chicken is cooked through, about 3 minutes on each side. Transfer the chicken to a plate.
Cook the pasta to al dente in a pot of salted boiling water according to package directions. Drain, reserving about 1/2 cup of the pasta water.
Meanwhile, increase the heat under the skillet to high, add the olive oil and garlic and cook, stirring until golden, being careful not to burn it, about 1 minute. Add the tomatoes, 1/8 teaspoon salt, and black pepper to taste, and reduce the heat to medium-low. Cook, stirring until the tomatoes become tender, 5-6 minutes.
Add the pasta to the tomatoes. If the pasta seems too dry, add some of the reserved pasta water. Add the chicken and toss well. Remove the pan from the heat, stir int he fresh basil and cheese, and serve hot.