Continuous glucose monitors (CGM) provide patients and clinicians with valuable insights about glycemic control that aid in diabetes management. The advent of large language models (LLMs), such as GPT-4, has enabled real-time text generation and summarization of medical data. Further, recent advancements have enabled the integration of data analysis features in chatbots, such that raw data can be uploaded and analyzed when prompted. Studying both the accuracy and suitability of LLM-derived data analysis performed on medical time series data, such as CGM data, is an important area of research. The objective of this study was to assess the strengths and limitations of using an LLM to analyze raw CGM data and produce summaries of 14 days of data for patients with type 1 diabetes. This study used simulated CGM data from 10 different cases. We first evaluated the ability of GPT-4 to compute quantitative metrics specific to diabetes found in an Ambulatory Glucose Profile (AGP). Then, using two independent clinician graders, we evaluated the accuracy, completeness, safety, and suitability of qualitative descriptions produced by GPT-4 across five different CGM analysis tasks. We demonstrated that GPT-4 performs well across measures of accuracy, completeness, and safety when producing summaries of CGM data across all tasks. These results highlight the capabilities of using an LLM to produce accurate and safe narrative summaries of medical time series data. We highlight several limitations of the work, including concerns related to how GPT-4 may misprioritize highlighting instances of hypoglycemia and hyperglycemia. Our work serves as a preliminary study on how generative language models can be integrated into diabetes care through CGM analysis, and more broadly, the potential to leverage LLMs for streamlined medical time series analysis.