Large Language Models (LLMs) are fast becoming indispensable tools for software developers, assisting or even partnering with them in crafting complex programs. The advantages are evident -- LLMs can significantly reduce development time, generate well-organized and comprehensible code, and occasionally suggest innovative ideas that developers might not conceive on their own. However, despite their strengths, LLMs will often introduce significant errors and present incorrect code with persuasive confidence, potentially misleading developers into accepting flawed solutions. In order to bring LLMs into the software development cycle in a more reliable manner, we propose a methodology for combining them with ``traditional'' software engineering techniques in a structured way, with the goal of streamlining the development process, reducing errors, and enabling users to verify crucial program properties with increased confidence. Specifically, we focus on the Scenario-Based Programming (SBP) paradigm -- an event-driven, scenario-based approach for software engineering -- to allow human developers to pour their expert knowledge into the LLM, as well as to inspect and verify its outputs. To evaluate our methodology, we conducted a significant case study, and used it to design and implement the Connect4 game. By combining LLMs and SBP we were able to create a highly-capable agent, which could defeat various strong existing agents. Further, in some cases, we were able to formally verify the correctness of our agent. Finally, our experience reveals interesting insights regarding the ease-of-use of our proposed approach. The full code of our case-study will be made publicly available with the final version of this paper.