Brown the chicken in oil. In a saucepan, add flour and salt to butter. Stir in chicken broth and cook until thick. Remove from heat; add cream and Tabasco.
Place asparagus in the bottom of a 9x13" casserole. Arrange the chicken on top of the asparagus. Pour sauce over the chicken and asparagus. Sprinkle with cheese. Bake at 350 for 45 minutes. Serves 6.