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I just talked to customer information at McIlhenny, the makers of
Tabasco sauces.  At first she was not too sure of what I was saying, I
had to spell out gluten.  But, she did say the vinegar was from
corn-mostly.  And, that yes, it was gluten free.

I was reminded by a chemistry teacher that ethyl acohol, which is the
source of quite a bit of distilled vinegar can be made from different
sources including corn or petroleum distillates.  So, if you have corn
problems (like me) be forewarned.
cbh in sunny and breezy Montana