This article introduces a recently created adaptation of the red-tailed hawk (RTH) algorithm. The proposed approach is a modified version of the original RTH algorithm, incorporating chaotic elements to enhance its integrity and performance. The RTH algorithm emulates the hunting behavior of the red-tailed hawk. This article demonstrates the adjustment of the power system stabilizer using the suggested technique in a case study involving a single-machine system. The suggested method was validated by benchmarking against known functions and evaluating its performance on a single-machine system in terms of transient responsiveness. The essay employs the original RTH algorithm as a means of comparison. The simulation results demonstrate that the proposed technique exhibits promising performance.