Does chewing gum make you fart?

Yes.

Chewing gum stimulates your saliva glands and it increases peristalsis, the forward motion of your GI tract.

Once your GI tract is moving properly the gas created by that darling bacteria that lives there also moves forward and exits giving you that golden toot.

Here's a link -

http://news.bbc.co.uk/2/hi/health/7568724.stm

"golden toot" hahaha, that gave me a "golden giggle"!

 Thanks for the link!

It's possible.  Sugar free chewing gum is sweetened with sugar alcohols, which can - in sufficient doses - cause massive gas.  The kind that could frighten farm animals.  SERIOUSLY.

To achieve this, however, one would have to several pieces of gum a day.  Swallowing air would make it worse, of course, but the sugar alcohols (sorbitol, mannitol, erythritol, and isomalt) are the real culprit.

Yes.  Quite a bit in fact.  Especially if it is sugar free gum. 

Not only have I conducted vast experiments in this field, but my husband can provide testimony as to the results. 

If  you're chewing a lot of sugar free gum, the artificial sweeteners can definitely give you gas!

Interesting.  Sugar alcohols give me diarrhea when I eat them in large quantities.  The worst episode I ever had was when I once ate some SF ice cream.