Peel the horseradish with a sturdy vegetable peeler or paring knife and cut it into chunks. Put in a food processor with about half the vinegar. Process, stopping the machine and scraping the mixture down as needed, until finely minced. (Do not try this with a blender; it will not work. The only alternative is to grate the horseradish by hand.)

Taste and add more vinegar as needed and salt to taste. Store in the refrigerator. Horseradish will keep almost indefinitely, but will become increasingly mild.