Bring peaches, vinegar, and honey to a simmer in a large saucepan. Cook, stirring occasionally, for 15 minutes. Cover, and let cool completely.
Working in batches, puree peach mixture in a food processor until smooth, about 10 seconds. Strain through a fine sieve into a large nonreactive bowl. Line sieve with cheesecloth, and place over another large nonreactive bowl. Pour strained peach mixture into sieve. (Do not press solids in sieve.) Cover with plastic wrap, and let mixture strain in refrigerator overnight (or up to 2 days).
Uncover, and remove sieve from bowl. Discard solids. Pour peach vinegar into a resealable nonreactive bottle or jar. (Vinegar can be refrigerated for up to 1 month.)