With more event datasets being released online, safeguarding the event dataset against unauthorized usage has become a serious concern for data owners. Unlearnable Examples are proposed to prevent the unauthorized exploitation of image datasets. However, it's unclear how to create unlearnable asynchronous event streams to prevent event misuse. In this work, we propose the first unlearnable event stream generation method to prevent unauthorized training from event datasets. A new form of asynchronous event error-minimizing noise is proposed to perturb event streams, tricking the unauthorized model into learning embedded noise instead of realistic features. To be compatible with the sparse event, a projection strategy is presented to sparsify the noise to render our unlearnable event streams (UEvs). Extensive experiments demonstrate that our method effectively protects event data from unauthorized exploitation, while preserving their utility for legitimate use. We hope our UEvs contribute to the advancement of secure and trustworthy event dataset sharing.