The number of connected devices contributing to the Internet of Things (IoT) has grown exponentially due to recent developments in wireless technology. The advent of IoT adds an entirely new category of applications to current services. Since the services are regulated by contact among objects, advantages are now being enhanced by utilizing these services. Many sensors and things are installed to track one or more activities. Hence, the load balancing protocol is essential in wireless IoT device architecture. To meet the QoS needs of IoT applications, it is crucial to measure, balance, analyze, and optimize these devices. Moreover, the IoT's vast amount of data and its processing can result in network outages. Studies on load balancing have primarily been conducted on cloud-based systems, and this challenge is an NP-hard problem. Consequently, this paper suggests a new energy-aware method for balancing the load on wireless IoT devices using a biogeography-inspired algorithm named Biogeography-Based Optimization (BBO) based on chaos theory. The BBO algorithm can become trapped in local optima. Chaos theory is one of the most effective techniques for improving the performance of evolutionary algorithms in terms of both the avoidance of local optimums and the rate of convergence. Therefore, the combination of these algorithms is suggested in this paper to improve the efficiency of the balancing method. The effectiveness of the method is simulated using MATLAB. Related current methods are compared to the proposed method, and the findings showed substantial improvements in delay time and load balancing using the proposed technique. The proposed method has decreased the delay time and energy consumption by 7.58% and 15% compared to other methods.