We present first experimental results from the \textit{Turing Game}, a modern implementation of the original imitation game as proposed by Alan Turing in 1950. The Turing Game is a gamified interaction between two human players and one AI chatbot powered by state-of-the-art Large Language Models (LLMs). The game is designed to explore whether humans can distinguish between their peers and machines in chat-based conversations, with human players striving to identify fellow humans and machines striving to blend in as one of them. To this end, we implemented a comprehensive framework that connects human players over the Internet with chatbot implementations. We detail the experimental results after a public launch at the Ars Electronica Festival in September 2024. While the experiment is still ongoing, in this paper we present our initial findings from the hitherto gathered data. Our long term vision of the project is to deepen the understanding of human-AI interactions and eventually contribute to improving LLMs and language-based user interfaces.