Out-of-distribution (OOD) detection plays a vital role in enhancing the reliability of machine learning models. As large language models (LLMs) become more prevalent, the applicability of prior research on OOD detection that utilized smaller-scale Transformers such as BERT, RoBERTa, and GPT-2 may be challenged, due to the significant differences in the scale of these models, their pre-training objectives, and the paradigms used for inference. This paper initiates a pioneering empirical investigation into the OOD detection capabilities of LLMs, focusing on the LLaMA series ranging from 7B to 65B in size. We thoroughly evaluate commonly used OOD detectors, examining their performance in both zero-grad and fine-tuning scenarios. Notably, we alter previous discriminative in-distribution fine-tuning into generative fine-tuning, aligning the pre-training objective of LLMs with downstream tasks. Our findings unveil that a simple cosine distance OOD detector demonstrates superior efficacy, outperforming other OOD detectors. We provide an intriguing explanation for this phenomenon by highlighting the isotropic nature of the embedding spaces of LLMs, which distinctly contrasts with the anisotropic property observed in smaller BERT family models. The new insight enhances our understanding of how LLMs detect OOD data, thereby enhancing their adaptability and reliability in dynamic environments. We have released the source code at https://github.com/Awenbocc/LLM-OOD for other researchers to reproduce our results.