The long-term goal of this research is to develop self-driving e-scooter technology to increase sustainability, accessibility, and equity in urban mobility. Toward this goal, in this work, we design and implement a self-driving e-scooter with the ability to safely travel along a pre-planned route using automated, onboard control without a rider. We also construct an autonomous driving framework by synthesizing open-source robotics software libraries with custom-designed modules specific to an e-scooter, including path planning and state estimation. The hardware and software development steps along with design choices and pitfalls are documented. Results of real-world autonomous navigation of our retrofitted e-scooter, along with the effectiveness of our localization methods are presented.