Cross-domain Sequential Recommendation (CDSR) aims to extract the preference from the user's historical interactions across various domains. Despite some progress in CDSR, two problems set the barrier for further advancements, i.e., overlap dilemma and transition complexity. The former means existing CDSR methods severely rely on users who own interactions on all domains to learn cross-domain item relationships, compromising the practicability. The latter refers to the difficulties in learning the complex transition patterns from the mixed behavior sequences. With powerful representation and reasoning abilities, Large Language Models (LLMs) are promising to address these two problems by bridging the items and capturing the user's preferences from a semantic view. Therefore, we propose an LLMs Enhanced Cross-domain Sequential Recommendation model (LLM4CDSR). To obtain the semantic item relationships, we first propose an LLM-based unified representation module to represent items. Then, a trainable adapter with contrastive regularization is designed to adapt the CDSR task. Besides, a hierarchical LLMs profiling module is designed to summarize user cross-domain preferences. Finally, these two modules are integrated into the proposed tri-thread framework to derive recommendations. We have conducted extensive experiments on three public cross-domain datasets, validating the effectiveness of LLM4CDSR. We have released the code online.