The main chemical ingredients of baking soda and
vinegar are sodium bicarbonate and acetic
acid, respectively. These chemicals can be
found in nature and have been used for a variety
of purposes since ancient times.
Because they produce carbon dioxide bubbles
when mixed, these and other similar chemicals have
been used as chemical leavening agents in
bread. The use of chemical leaveners appears
to have been first documented as early as 1796
in a cookbook called "American Cookery".
Although, I'm not sure whether or not it is known
who was the very first person to put baking soda
and vinegar together and observe their reaction.