The theoretically proven security of quantum key distribution(QKD) could revolutionize the way in which information exchange is protected in the future(1,2). Several field tests of QKD have proven it to be a reliable technology for cryptographic key exchange and have demonstrated nodal networks of point-to-point links(3-5). However, until now no convincing answer has been given to the question of how to extend the scope of QKD beyond niche applications in dedicated high security networks. Here we introduce and experimentally demonstrate the concept of a 'quantum access network': based on simple and cost-effective telecommunication technologies, the scheme can greatly expand the number of users in quantum networks and therefore vastly broaden their appeal. We show that a high-speed single-photon detector positioned at a network node can be shared between up to 64 users for exchanging secret keys with the node, thereby significantly reducing the hardware requirements for each user added to the network. This point-to-multipoint architecture removes one of the main obstacles restricting the widespread application of QKD. It presents a viable method for realizing multi-user QKD networks with efficient use of resources, and brings QKD closer to becoming a widespread technology.