Cut and scrape flesh from watermelon rind; reserve for another use. Cut away outer green skin from rind; discard. Cut rind into 1-inch pieces. (You should have about 9 cups.)
Bring rind, vinegar, sugar, water, ginger, peppercorns, chiles, and salt to a boil in a large saucepan. Reduce heat, and simmer until rind is translucent and tender and liquid is syrupy, about 55 minutes. Divide mixture among 2 pint-size and one 1/2-pint-size sterilized glass jars; refrigerate.
Chutney can be refrigerated for up to 3 weeks. To preserve it longer (up to 1 year), use white-wine vinegar (at least 5 percent acidity), which is more acidic than rice vinegar, and can it in a water bath.