[SpartanAir]

Choices and Whole Foods have aspartame-free gum. It's not nearly as cheap as most gum and doesn't last as long but it can be ok.

From Wikipedia:

"Upon ingestion, aspartame breaks down into natural residual components, including aspartic acid, phenylalanine, methanol,[25] and further breakdown products including formaldehyde[26] and formic acid, accumulation of the latter being suspected as the major cause of injury in methanol poisoning. Human studies show that formic acid is excreted faster than it is formed after ingestion of aspartate. In some fruit juices, higher concentrations of methanol can be found than the amount produced from aspartame in beverages.[13]"