The integration of large language models (LLMs) with geographic information science (GIScience) represents a new frontier in interdisciplinary research that combines advanced natural language processing with sophisticated spatial data analysis. This paper explores the synergistic potential of combining the natural language understanding and generation capabilities of LLMs with the expertise of GIScience in handling complex geospatial data. By exploring the specific contributions that LLMs can offer to GIScience, such as improving data processing, analysis, and visualization, and the mutual benefits that GIScience can offer to LLMs in terms of spatial reasoning and conceptual frameworks, we outline a comprehensive framework and a research agenda for this integration. Furthermore, we address the societal and ethical implications of this convergence, highlighting the challenges of bias, misinformation, and environmental impact. Through this exploration, we aim to set the stage for innovative applications in urban planning, environmental analysis, and beyond, while emphasizing the need for responsible use of AI.