Search engines play an important role on the Web, helping users find relevant resources and answers to their questions. At the same time, search logs can also be of great utility to researchers. For instance, a number of recent research efforts have relied on them to build prediction and inference models, for applications ranging from economics and marketing to public health surveillance. However, companies rarely release search logs, also due to the related privacy issues that ensue, as they are inherently hard to anonymize. As a result, it is very difficult for researchers to have access to search data, and even if they do, they are fully dependent on the company providing them. Aiming to overcome these issues, this paper presents Private Data Donor (PDD), a decentralized and private-by-design platform providing crowd-sourced Web searches to researchers. We build on a cryptographic protocol for privacypreserving data aggregation, and address a few practical challenges to add reliability into the system with regards to users disconnecting or stopping using the platform. We discuss how PDD can be used to build a flu monitoring model, and evaluate the impact of the privacy-preserving layer on the quality of the results. Finally, we present the implementation of our platform, as a browser extension and a server, and report on a pilot deployment with real users.