Thanks to the rapid progress and growing complexity of quantum algorithms, correctness of quantum programs has become a major concern. Pioneering research over the past years has proposed various approaches to formally verify quantum programs using proof systems such as quantum Hoare logic. All these prior approaches are post-hoc: one first implements a complete program and only then verifies its correctness. In this work, we propose Quantum Correctness by Construction (QbC): an approach to constructing quantum programs from their specification in a way that ensures correctness. We use pre- and postconditions to specify program properties, and propose a set of refinement rules to construct correct programs in a quantum while language. We validate QbC by constructing quantum programs for two idiomatic problems, teleportation and search, from their specification. We find that the approach naturally suggests how to derive program details, highlighting key design choices along the way. As such, we believe that QbC can support the design of quantum algorithms and software.