The ability to predict drug overdose risk from a patient's medical records is crucial for timely intervention and prevention. Traditional machine learning models have shown promise in analyzing longitudinal medical records for this task. However, recent advancements in large language models (LLMs) offer an opportunity to enhance prediction performance by leveraging their ability to process long textual data and their inherent prior knowledge across diverse tasks. In this study, we assess the effectiveness of Open AI's GPT-4o LLM in predicting drug overdose events using patients' longitudinal insurance claims records. We evaluate its performance in both fine-tuned and zero-shot settings, comparing them to strong traditional machine learning methods as baselines. Our results show that LLMs not only outperform traditional models in certain settings but can also predict overdose risk in a zero-shot setting without task-specific training. These findings highlight the potential of LLMs in clinical decision support, particularly for drug overdose risk prediction.