Trim asparagus spears to be roughly the same length.
Bring a large pot of salted water to a boil over high heat. Add trimmed asparagus spears. Boil 2 minutes. Immediately transfer asparagus to an ice cold water bath to stop the cooking and set the color. Drain.
With a very sharp knife, cut each chicken breast in half horizontally to make 2 thin cutlets out of each breast. Pound each cutlet to create an even thickness across the breast.
Begin to layer remaining ingredients on top of chicken breast cutlets. Begin by spreading 1 Tablespoon of pesto on each piece of chicken. Top with cheese, prosciutto and 4-5 asparagus spears.
Starting on one side of the chicken breast, begin to roll up ingredients around the asparagus. If the rolls do not stay together, secure with a toothpick. Season roll ups with salt and pepper to taste.
In a large skillet, heat olive oil over medium high heat. Add chicken rolls and cover. Cook 4-5 minutes. Turn the roll ups. Cover. Cook for an additional 4-5 minutes or until chicken is done.
Transfer to a serving plate.