Harris hawks optimization (HHO) is a population-based metaheuristic algorithm, inspired by the hunting strategy and cooperative behavior of Harris hawks. In this study, HHO is hybridized with 10 different chaotic maps to adjust its critical parameters. Hybridization is performed using four different methods. First, 15 test functions with unimodal and multimodal features are used for the analysis to determine the most successful chaotic map and the hybridization method. The results obtained reveal that chaotic maps increase the performance of HHO and show that the piecewise map method is the most effective one. Moreover, the proposed chaotic HHO is compared to four metaheuristic algorithms in the literature using the CEC2019 set. Next, the proposed chaotic HHO is applied to three mechanical design problems, including pressure vessel, tension/compression spring, and three-bar truss system as benchmarks. The performances and results are compared with other popular algorithms in the literature. They show that the proposed chaotic HHO algorithm can compete with HHO and other algorithms on solving the given engineering problems very successfully.