Doug Rauch, a former president of Trader Joe’s, thinks he has a partial solution to the problem: Sell food past its “best by” date. Contrary to widespread belief, such stamps are not expiration dates or markers of food safety—and, with the exception of infant formula, are not federally mandated. Rather, the sell-by date is supposed to indicate the point after which the peak quality can no longer be guaranteed. Much of the time, the food remains good way past then—that is, until stores throw it away. (Super­markets pull an estimated $2,300 worth of food off their shelves daily that is past its date stamp, according to Jonathan Bloom, author of the 2010 American Wasteland.)

So this fall Rauch plans to open a store in Boston that will sell it. By procuring food from outlets like grocers, growers, and manufacturers that is past or nearing its best-by date and then turning most of it into affordable grab-and-go meals, Rauch hopes to solve two problems: food waste and a more pressing one—hunger. About one in six American households don’t get enough to eat, according to the USDA. Rauch, however, is going after an even bigger market: He wants to serve those who are getting enough calories, but the wrong kind (soda, snacks, etc.). And by structuring his nonprofit as a grocery store—called Daily Table—instead of a food bank, he hopes the model will be sustainable. “With most hunger relief, you have to qualify for services,” Rauch says. “This flips it and says, ‘I have to earn your patronage every day.’ ”

Rauch might be on to something. The European Union is considering scrapping best-before dates on items like hard cheeses and pasta—a move that could reduce Europe’s food ­waste by 15%.

This story is from the September 22, 2014 issue of Fortune.