Title: Undistillable: Making A Nasty Teacher That CANNOT teach students. Abstract: Knowledge Distillation (KD) is a widely used technique to transfer knowledge from pre-trained teacher models to  (usually more lightweight) student models. However, in certain situations, this technique is more of a curse than a blessing. For instance, KD poses a potential risk of exposing intellectual properties (IPs): even if a trained machine learning model is released in ``black boxes'' (e.g., as executable software or APIs without open-sourcing code), it can still be replicated by KD through imitating input-output behaviors. To prevent this unwanted effect of KD, this paper introduces and investigates a concept called $\textit{Nasty Teacher}$: a specially trained teacher network that yields nearly the same performance as a normal one, but would significantly degrade the performance of student models learned by imitating it. We propose a simple yet effective algorithm to build the nasty teacher, called $\textit{self-undermining knowledge distillation}$. Specifically, we aim to maximize the difference between the output of the nasty teacher and a normal pre-trained network. Extensive experiments on several datasets demonstrate that our method is effective on both standard KD and data-free KD, providing the desirable KD-immunity to model owners for the first time. We hope our preliminary study can draw more awareness and interest in this new practical problem of both social and legal importance. Our codes and pre-trained models can be found at: $\url{https://github.com/VITA-Group/Nasty-Teacher}$.