In a large pot of salted boiling water, cook angel hair pasta until it is al dente, about 8 to 10 minutes. Drain, and set aside.
In a large skillet, heat oil over medium-high heat. Saute the onions and garlic. Stir in the tomatoes, chicken, basil, salt and hot pepper sauce. Reduce heat to medium, and cover skillet. Simmer for about 5 minutes, stirring frequently, until mixture is hot and tomatoes are soft.
Toss sauce with hot cooked angel hair pasta to coat. Serve with Parmesan cheese.