The first bricks-and-mortar shop in Washington, D.C. to institute a mobile app that allows customers to establish an ongoing tab is in Penn Quarter: Chinatown Coffee Company.
The mobile app, called Card Case from Square, provides an alternative to cash or credit cards.
The customer activates the app while inside the coffee shop and it verifies your location. The barista then pulls up your tab on an iPad, charges your purchase, and ultimately your credit card is charged. The receipt appears on your phone nearly instantly. Pretty cool.