Pound the chicken pieces to 1 cm thickness. Melt the butter or margarine in a fry pan over medium-high temperature. Add chicken and cook, turning, for about 5 minutes or until the chicken is brown. Remove chicken and set aside.
To the drippings remaining in the fry pan, add the asparagus and mushrooms and cook, stirring, for about 3 minutes. Return the chicken to the pan, add the Marsala wine, water, salt, and pepper. Bring the mixture to a boil and boil for 2 minutes to reduce the liquid.
Reduce heat, cover and simmer for about 3 minutes or until the chicken and vegetables are tender.
Arrange the chicken on a serving platter. Spoon the vegetable sauce over the chicken. Sprinkle with chopped parsley and serve.