Software is now a key component present in all aspects of our society. Its preservation has attracted growing attention over the past years within the digital preservation community. We claim that source code—the only representation of software that contains human readable knowledge—is a precious digital object that needs special handling: it must be a first class citizen in the preservation landscape and we need to take action immediately, given the increasingly more frequent incidents that result in permanent losses of source code collections. In this paper we present Software Heritage, an ambitious initiative to collect, preserve, and share the entire corpus of publicly accessible software source code. We discuss the archival goals of the project, its use cases and role as a participant in the broader digital preservation ecosystem, and detail its key design decisions. We also report on the project road map and the current status of the Software Heritage archive that, as of early 2017, has collected more than 3 billion unique source code files and 700 million commits coming from more than 50 million software development projects.