Heat 4 quarts salted water to boiling in large saucepan. Add angel hair pasta; cook until tender. Drain.
Meanwhile, cut chicken breasts into 1/4-inch-wide strips. Heat oil in 12-inch skillet over medium-high heat. Add chicken; cook until well browned on all sides, stirring frequently. Add cherries, brandy, green onions, TABASCO® Sauce and salt; heat to boiling over high heat. Reduce heat to low; simmer 5 minutes to blend flavors, stirring occasionally. Stir in cream; heat through. Toss with angel hair pasta.