This paper addresses the challenge of forecasting chaotic processes monitored by an unstable system. The presence of chaotic components in observation series significantly limits the effectiveness of traditional statistical data analysis methods, necessitating new, unconventional approaches to forecasting. The proposed implementation of a forecasting software and algorithmic complex is based on a multi-expert data analysis system. Preliminary forecasts are generated by software experts functioning as weak classifiers. The terminal forecasting decision is made by a supervising expert through the combined processing of results from a group of independent software experts. In machine learning terminology, this forecasting scheme aligns with a stacking algorithm within ensemble decision-making technology. Our approach demonstrates the potential for improved forecasting accuracy in chaotic environments by leveraging the structural redundancy of multi-expert systems. Empirical results show that this method can effectively enhance the robustness of predictive decisions, offering a promising direction for future research in managing unpredictability in chaotic systems.