San Francisco's Radius Cafe is one of those places where "local" is the rule—all the food is sourced within a 100-mile radius of the restaurant. So it's a touch ironic to meet there with Brian Chesky, the hoodie-wearing 32-year-old co-founder of Airbnb, whose game plan is global.

Airbnb is a Web service that lets travelers book couches, beds, rooms, houses, boats and even castles on a nightly basis. In six years Airbnb has become a company valued at $2.5 billion, with 500,000 properties available in more than 190...