An emerging literature suggests Artificial Intelligence (AI) can greatly enhance autocrats' repressive capabilities and strengthen their control. This paper argues that AI’s ability to do so may be hampered by existing repressive institutions. In particular, I suggest that autocrats suffer from an "authoritarian data problem," in which citizens' strategic behavior under repression diminishes the amount of useful information in the data for training AI. This poses a fundamental limitation for AI's usefulness in authoritarian control - the more repression there is, the less information there will be in AI's training data, and the worse AI will perform. I illustrate this argument using an AI experiment and censorship data in China. I show that AI's accuracy in censorship decreases with increasing repression, especially during times of political crisis. I further show that this problem cannot be easily fixed with more data. Ironically, however, the existence of the free world can help boost AI's ability to censor.