In this paper, a decentralized chemical-source localization method is presented. In a real-world scenario, many challenges arise, including sporadic chemical measurements due to the complex interactions between the unmanned aerial vehicles (UAVs), the ambient air, and obstacles. The localization method is split into two phases: a search phase, where the agents cover the area and look for an initial chemical reading; followed by a convergence phase, where UAV agents utilize a particle swarm optimization (PSO) algorithm to locate the source of the chemical leak. The decentralized source-localization method enables a swarm of UAVs to safely travel in a complex environment and avoid obstacles and other agents while searching for the leaking source. The method is validated in simulation using realistic dynamic chemical plumes and through outdoor flight tests using a swarm of UAVs. The results demonstrate the feasibility of the approach.