CLAYTON, Mo. — The country’s latest experiment in pay-what-you-want eating started last weekend when a cafe run by Panera Bread, one of the fastest-growing chain restaurants in the country, began refusing payments from customers in this affluent St. Louis suburb and politely asked them instead to “take what you need, leave your fair share” in wood-and-plexiglass lockboxes.

There was a line out the door at the peak of the lunch rush — a crew of government workers, area professionals and the merely curious who seemed enthusiastic, if a little bewildered, about the enterprise. Was this a high-class soup kitchen? A newfangled charity?

Neither, it turned out. It is one of about a dozen operations around the country providing free or low-cost food to those who need it and trying to sustain themselves off the money their paying customers decide to toss in the box.

Some will call it a hot trend, others a pipe dream, but the notion of letting diners choose what they pay for their meals has been gaining traction over the last decade as an outgrowth of the organic food movement and the advent of social entrepreneurs — those who believe that making a profit and doing good are not mutually exclusive.