Bring four quarts water and 1 tablespoon salt to boil; add pasta and cook according to package directions, about 2 to 3 minutes. Drain well and transfer to a serving bowl.
Meanwhile, in a large non-stick skillet over medium-high heat, heat olive oil until shimmering. Add chicken and shallots and cook until the chicken is mostly cooked through and the shallots have softened, about 5 minutes.
Reduce heat to medium and stir in wine and cream. Cook, stirring frequently, until sauce begins to thicken, about 3 minutes. Stir in tomatoes, basil, Parmesan cheese, and salt and pepper to taste (I like 1/2 teaspoon salt and 1/4 teaspoon pepper.)
Pour chicken and cream sauce over pasta in serving bowl. Garnish with additional Parmesan cheese and fresh basil and serve.