We present the first experiments on Native Language Identification (NLI) using LLMs such as GPT-4. NLI is the task of predicting a writer's first language by analyzing their writings in a second language, and is used in second language acquisition and forensic linguistics. Our results show that GPT models are proficient at NLI classification, with GPT-4 setting a new performance record of 91.7% on the benchmark TOEFL11 test set in a zero-shot setting. We also show that unlike previous fully-supervised settings, LLMs can perform NLI without being limited to a set of known classes, which has practical implications for real-world applications. Finally, we also show that LLMs can provide justification for their choices, providing reasoning based on spelling errors, syntactic patterns, and usage of directly translated linguistic patterns.