ChatGPT, as an advanced model that seamlessly integrates into diverse digital interactions, shows great potential to enhance the performance of consumer technology and reshape its landscape. The critical question of its trustworthiness and associated challenges becomes increasingly prominent. However, the literature still lacks a thorough review to study its trust. This comprehensive review explores whether ChatGPT is trustworthy enough by navigating the multifaceted realm of large language models, placing a significant focus on its exemplar model, ChatGPT. Our exploration traverses the complex interplay of factors impacting user trust, including trust in ChatGPT itself and trust in its utilization and dissemination. By delving into insightful perspectives on the ChatGPT trustworthiness regarding a set of evaluation criteria including fundamental properties, subjective properties, security and privacy, we find that ChatGPT is far from trustworthy based on related literature review. This paper sheds light on the weakness of ChatGPT trust and provides the trajectory of future development in the realm of large language models.