A central challenge in building continually improving agents is that training environments are typically static or manually constructed. This restricts continual learning and generalization beyond the training distribution. We address this with COvolve, a co-evolutionary framework that leverages large language models (LLMs) to generate both environments and agent policies, expressed as executable Python code. We model the interaction between environment and policy designers as a two-player zero-sum game, ensuring adversarial co-evolution in which environments expose policy weaknesses and policies adapt in response. This process induces an automated curriculum in which environments and policies co-evolve toward increasing complexity. To guarantee robustness and prevent forgetting as the curriculum progresses, we compute the mixed-strategy Nash equilibrium (MSNE) of the zero-sum game, thereby yielding a meta-policy. This MSNE meta-policy ensures that the agent does not forget to solve previously seen environments while learning to solve previously unseen ones. Experiments in urban driving, symbolic maze-solving, and geometric navigation showcase that COvolve produces progressively more complex environments. Our results demonstrate the potential of LLM-driven co-evolution to achieve open-ended learning without predefined task distributions or manual intervention.