Context: Technical debt management is challenging for software engineers due to poor tool support and a lack of knowledge on how to prioritize technical debt repayment and prevention activities. Furthermore, when there is a large backlog of debt, developers often lack the motivation to address it. Objective: In this paper, we describe a design study to investigate how gamification can support Technical Debt Management in a large legacy software system of an industrial company. Our study leads to a novel tool (named Themis) that combines technical debt support, version control, and gamification features. In addition to gamification features, Themis provides suggestions for developers on where to focus their effort, and visualizations for managers to track technical debt activities. Method: We describe how Themis was refined and validated in an iterative deployment with the company, finally conducting a qualitative study to investigate how the features of Themis affect technical debt management behavior. We consider the impact on both developers and managers. Results: Our results show that it achieves increased developer motivation, and supports managers in monitoring and influencing developer behaviors. We show how our findings may be transferable to other contexts by proposing guidelines on how to apply gamification. Conclusions: With this case, gamification appears as a promising solution to help technical debt management, although it needs to be carefully designed and implemented to avoid its possible negative effects.