Like medicine, psychology, or education, data science is fundamentally an applied discipline, with most students who receive advanced degrees in the field going on to work on practical problems. Unlike these disciplines, however, data science education remains heavily focused on theory and methods, and practical coursework typically revolves around cleaned or simplified data sets that have little analog in professional applications. We believe that the environment in which new data scientists are trained should more accurately reflect that in which they will eventually practice, and we propose here a data science master's degree program that takes inspiration from the residency model used in medicine. Students in the suggested program would spend their time working on a practical problem with an industry, government, or nonprofit partner, supplemented with coursework in data science methods and theory. We also discuss how this program can also be implemented in shorter formats to augment existing professional master's programs in different disciplines. This approach to learning by doing is designed to fill gaps in our current approach to data science education and ensure that students develop the skills they need to practice data science in a professional context and under the many constraints imposed by that context.