Computational creativity is an emerging branch of artificial intelligence that places computers in the center of the creative process. Broadly, creativity involves a generative step to produce many ideas and a selective step to determine the ones that are the best. Many previous attempts at computational creativity, however, have not been able to achieve a valid selective step. This paper shows how bringing data sources from the creative domain and from hedonic psychophysics together with machine learning and data analytics techniques can overcome this shortcoming to yield a system that can produce novel and high-quality creative artifacts. To demonstrate our data-driven approach, we developed and deployed a computational creativity system for culinary recipes and menus, Chef Watson, which can operate either autonomously or semiautonomously with human interaction. We present the basic system architecture, data engineering, and algorithms that are involved. Experimental results demonstrate the system passes the test for creativity based on the consensual assessment technique, producing a novel and flavorful recipe. Large-scale deployments are also discussed.