Place a large, tall-sided skillet with 1 to 2 inches of water over high heat and bring up to a boil to cook the asparagus.
Working with one chicken breast at a time, line the breast with the tip closest to you. Place your hand flat on top of it and, with a very sharp knife, cut into the center of the thickest part of the breast. Carefully and slowly, work your way down to the tip end, cutting into the chicken. The goal is to butterfly the breasts, cutting them just shy of completely in half. Open up the chicken breast as if it were a book and pound it out slightly under a piece of plastic wrap with a heavy skillet. Repeat with the remaining chicken.