Over the last decade, course-based undergraduate research experiences (CUREs) have been recognized as a way to improve undergraduate science, technology, engineering, and mathematics education by engaging students in authentic discovery. CUREs have been shown to have positive benefits similar to traditional undergraduate research experiences; however, they can reach a larger number of students and are open to all students who enroll in the course. Motivated by the need to redesign the large introductory physics lab at The University of Colorado-Boulder to be fully remote in response to the COVID-19 pandemic, we designed and implemented the first remote, large-enrollment, physics CURE. Here, we detail the motivations and the challenges when designing the course, and provide detailed descriptions of the course components. Throughout the course, we collected course artifacts and administered surveys to the students. Based on these data sources, we find that this course helped students gain research skills and coding confidence, engage in productive and enjoyable teamwork experiences, and feel motivated and interested in experimental physics research.