To address the issues of UAV path planning being susceptible to local optima and low convergence precision in complex three-dimensional environments, a path planning method based on the Chaotic Enhanced Leader Slime Mould Algorithm (CELSMA) is proposed. Firstly, a triple-leader mechanism and a Logistic chaotic mapping perturbation strategy are incorporated into the standard slime mould algorithm. By implementing chaotic population initialization, adaptive weight adjustment, and chaotic perturbation-based position update, the algorithm's global exploration capability and convergence performance are substantially improved. Secondly, a mathematical model for path planning with complex constraints is developed, taking into account multiple objectives including path length, threat avoidance, altitude constraints, and smoothness. Finally, the optimization performance of CELSMA is evaluated using benchmark functions, and simulations are carried out under various typical threat scenarios based on real digital elevation model data. The results indicate that the proposed method can generate feasible flight paths that are safe, smooth, and have lower overall costs in complex 3D environments. It achieves the best performance in terms of path length, threat avoidance capability, and flight stability, thereby validating the superiority and robustness of CELSMA for UAV path planning.