An increasing amount of personal data is automatically gathered and stored on servers by administrations, hospitals, insurance companies, etc. Citizen themselves often count on internet companies to store their data and make them reliable and highly available through the internet. However, these benefits must be weighed against privacy risks incurred by centralization. This paper suggests a radically different way of considering the management of personal data. It builds upon the emergence of new portable and secure devices combining the security of smart cards and the storage capacity of NAND Flash chips. By embedding a full-fledged Personal Data Server in such devices, user control of how her sensitive data is shared by others (by whom, for how long, according to which rule, for which purpose) can be fully reestablished and convincingly enforced. To give sense to this vision, Personal Data Servers must be able to interoperate with external servers and must provide traditional database services like durability, availability, query facilities, transactions. This paper proposes an initial design for the Personal Data Server approach, identifies the main technical challenges associated with it and sketches preliminary solutions. We expect that this paper will open exciting perspectives for future database research.