The problem is that there are a lot of things which can ferment to make vinegar, including things which can't be eaten like wheat and rye. The OU guide lists several brands of balsamic vinegar which they certify as kosher for passover (see the second link in the sources below).If you want a much longer explanation of how vinergar is made and the Jewish implications, see the article in the third source.ll extra virgin olive oils are Kosher for Passover, even without any Kosher supervision. All other oils (including olive oil) require a reliable Kosher certification to be consumed on Passover..