When you purchase a whole tenderloin from a grocer, chances are it will include the chain muscle attached to the loin. The chain, a fat-covered meat muscle, is used in beef stocks or sometimes left on the loin and sliced as part of tenderloin or filet mignon steaks. It is a much tougher piece of meat than the loin itself.
Hold the tenderloin over the sink and open the packaging. Most whole beef tenderloins come in vacuum packaging, but juices and blood can spill after opening.
Rinse the whole tenderloin under cold running water. Place the tenderloin on your cutting board and pat dry with paper towels.
Use a sharp knife to trim away all visible fat from the tenderloin.
Insert your fingers between the chain and the main loin and pull the chain away from the tenderloin. The chain is easily identifiable, as it is a separate muscle. Use the knife to cut away areas that are difficult to pull.
Insert the tip of your knife beneath the silverskin -- the membrane covering the tenderloin beneath where the chain was -- and slice the silverskin away from the loin. The tenderloin is now ready to slice or cook as desired.
Trim the fat away from the chain, taking care not to slice too far into the meat. Once the fat is removed, slice or cube the chain meat for use in stews, stir-fry or other dishes calling for beef.