Snap tough ends from asparagus and discard. Rinse asparagus and, if desired, peel stems with a vegetable peeler.
Rinse chicken, pat dry, and lay pieces 4 to 5 inches apart on a sheet of plastic wrap. Cover with more plastic wrap. Pound chicken with a flat mallet until it is 3/8 to 1/2 inch thick.
Put bread crumbs in a shallow pan. Turn chicken in crumbs to coat evenly, patting to make them stick.
Set an 11- to 12-inch ovenproof nonstick frying pan over high heat. When hot, add butter and swirl until melted. Add chicken and cook until browned on bottom, shaking pan to avoid scorching butter, about 2 minutes. Turn pieces over and cook 1 minute more.
Set pan in a 350° oven and bake until chicken is no longer pink in center (cut to test), 7 to 9 minutes.
Meanwhile, in a 10- to 12-inch frying pan over high heat, bring about 1 inch water to a boil. About 3 minutes before chicken is done, add asparagus to boiling water and cook just until tender when pierced; drain.
Quickly transfer each chicken breast half to a warm plate. Top with equal amounts of the crab and asparagus, and pour hollandaise sauce over each portion. Garnish with chives.