For deviled ham, in a food processor combine ham, mayonnaise, onion, tarragon, Worcestershire, vinegar, mustard, cayenne, and a few grinds of black pepper. Cover and process until ham is very finely chopped and almost smooth, scraping processor bowl as needed. Set aside while butterflying chicken breasts (see next step) or cover and refrigerate up to 2 days.
To butterfly chicken breasts, place each breast half on a flat surface or cutting board. With palm on chicken and fingers away from blade, cut through one side of the chicken breast to within 3/4 inch of the opposite side. Open to lie flat. Pound chicken with flat side of meat mallet to 1/4-inch thickness.
To stuff chicken breasts, spread 1/4 cup of the deviled ham on half of each chicken piece. Top with 3 to 5 asparagus spears. Fold unstuffed half over stuffing. Tie closed with 100-percent-cotton kitchen string. Sprinkle chicken with salt and pepper.
In a 12-inch skillet heat oil over medium heat. Cook chicken in hot oil for 10 to 12 minutes per side, until browned and no longer pink (170 degrees F).
If desired, serve chicken with a Mixed Green and Radish Salad.