Disassemble the barstool into its component parts, completely removing all pieces with a chrome finish for total access. Remove the padded seat as well, if possible. Use a screwdriver, wrench or drill, depending on what type of hardware is used to attach the stool.
Wipe down every chrome surface with a rag dipped in hot, soapy water. Scrub the surfaces vigorously to remove all dirt and debris.
Scrape persistently discolored or dirty sections with steel wool. Apply a paste of powdered cleanser such as Barkeepers Friend or Bon Ami to any discolored spots that don't lessen after vigorous steel wool work. Let the paste sit on the spot for a few minutes. Re-scrape with the steel wool, then rinse off all surfaces.
Apply chrome polish to a clean buffing cloth and begin polishing the chrome finish, working in tight, focused circles to cover the entire surface. Work back over each previously polished section, using a clean section of the cloth.
Apply a thin layer of wax to the chrome, using the buffing cloth. Apply wax to the surface in small, focused circles similar to the chrome polish. Buff until the wax residue cannot be seen.