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Recent work has demonstrated that pre-trained language models (PLMs) are zero-shot learners. However, most existing zero-shot methods involve heavy human engineering or complicated self-training pipelines, hindering their application to new situations. In this work, we show that zero-shot text classification can be improved simply by clustering texts in the embedding spaces of PLMs. Specifically, we fit the unlabeled texts with a Bayesian Gaussian Mixture Model after initializing cluster positions and shapes using class names. Despite its simplicity, this approach achieves superior or comparable performance on both topic and sentiment classification datasets and outperforms prior works significantly on unbalanced datasets. We further explore the applicability of our clustering approach by evaluating it on 14 datasets with more diverse topics, text lengths, and numbers of classes. Our approach achieves an average of 20% absolute improvement over prompt-based zero-shot learning. Finally, we compare different PLM embedding spaces and find that texts are well-clustered by topics even if the PLM is not explicitly pre-trained to generate meaningful sentence embeddings. This work indicates that PLM embeddings can categorize texts without task-specific fine-tuning, thus providing a new way to analyze and utilize their knowledge and zero-shot learning ability.