Recursive self-improvement (RSI) — the capacity of an AI system to improve its own performance across successive generations without external retraining or manual intervention — has been widely discussed as a theoretical milestone yet rarely demonstrated empirically. We present FELIX, a population-based artificial organism that achieves reproducible RSI across three successive generations under fixed rules and a staged environmental selection protocol. In five independent runs across five distinct random seeds, every run produced a full positive improvement chain: Gen 0 → Gen 1 → Gen 2, with each generation sustaining measurably higher fitness than the last. The mean improvement from Gen 0 to Gen 2 across all five runs was +129.7%, with a range of +86.3% to +188.0%. No external gradient, hyperparameter change, or code modification occurs between generations; all improvement arises from FELIX's internal dynamics. We present the experimental results, measurement protocol, and limitations of this demonstration. Implementation details are not disclosed at this time.