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Single domain generalization (single-DG) for medical image segmentation aims to learn a style-invariant representation, which can be generalized to a variety unseen target domains, with the data from a single source. However, due to the limitation of sample diversity in the single source domain, the robustness of generalized features yielded by existing single-DG methods is still unsatisfactory. In this paper, we propose a novel single-DG framework, namely Hallucinated Style Distillation (HSD), to generate the robust style-invariant feature representation. Particularly, our HSD firstly expands the style diversity of the single source domain via hallucinating the samples with random styles. Then, a hallucinated cross-domain distillation paradigm is proposed to distillate the style-invariant knowledge between the original and style-hallucinated medical images. Since the hallucinated styles close to the source domain may over-fit our distillation paradigm, we further propose a learning objective to diversify style-invariant representation, which alleviates the over-fitting issue and smooths the learning process of generalized features. Extensive experiments on two standard domain generalized medical image segmentation datasets show the state-of-the-art performance of our HSD. Source code will be publicly available.