There is widespread concern that economics does not attract as broad or diverse a pool of talent as it could. For example, less than one-third of undergraduates who receive degrees in economics are women, significantly lower than in math or statistics. This article presents a case study of a new introductory undergraduate course at Harvard, "Using Big Data to Solve Economic and Social Problems," that enrolled 400 students, achieved nearly a 50-50 gender balance, and was among the highest-rated courses in the college. We first summarize the course's content and pedagogical approach. We then illustrate how this approach differs from that taken in traditional courses by showing how canonical topics -- income inequality, tax incidence, and adverse selection -- are taught differently. Then, drawing upon students' comments and prior research on effective teaching practices, we identify elements of the course's approach that appear to underlie its success: connecting the material to students' own experiences; teaching skills that have social and career value; and engaging students in scientific investigation of real-world problems. We conclude by discussing how these ideas for improving instruction in economics could be applied in other courses and tested empirically in future research. [Additional funding for this research was provided by the Chan-Zuckerberg Initiative and Harvard University.]