The electricity system becomes more complex, connecting massive numbers of end-users and distributed generators. Adding or removing grid connections requires expert studies to align technical constraints with user requests. In times of labour shortages, carrying out these studies represents a significant amount of time that engineers at system operators spend in planning departments. As time is limited, only standard block connectivity contracts can be offered to end-users, or the requests pile up. Even if offers are made, these often do not perfectly match the user's requirements, leading to overpaying or underusing the grid capacity. This paper investigates whether end-users can negotiate individual, flexible time-of-use contracts directly with the grid using Large Language Models (LLMs) in chats at scale. This work addresses system-level technical challenges in automating contract design under grid constraints, integrating LLMs with power system models, and ensuring secure, reliable interaction. We develop a chat system using functional programs for power system analysis, enabling users to request customised, technically feasible contracts at scale. We demonstrate high accuracy in executing engineering studies, robustness to user input variations, self-assessment of connection requests by small and medium enterprises, and potential for secure, chat-enabled maintenance planning. This initial study paves the way toward developing a tailored LLM system, resulting in possible high-efficiency gains for grid planning and customer management. The code is available at: https://github.com/TU-Delft-AI-Energy-Lab/LLM-Electricity-Contracts