Detection of leaks of fugitive greenhouse gases (GHGs) from landfills and natural gas infrastructure is critical for not only their safe operation but also for protecting the environment. Current inspection practices involve moving a methane detector within the target area by a person or vehicle. This procedure is dangerous, time consuming, labor intensive and above all unavailable when access to the desired area is limited. Remote sensing by an unmanned aerial vehicle (UAV) equipped with a methane detector is a cost-effective and fast method for methane detection and monitoring, especially for vast and remote areas. This paper describes the integration of an off-the-shelf laser-based methane detector into a multi-rotor UAV and demonstrates its efficacy in generating an aerial methane concentration map of a landfill. The UAV flies a preset flight path measuring methane concentrations in a vertical air column between the UAV and the ground surface. Measurements were taken at 10 Hz giving a typical distance between measurements of 0.2 m when flying at 2 m/s. The UAV was set to fly at 25 to 30 m above the ground. We conclude that besides its utility in landfill monitoring, the proposed method is ready for other environmental applications as well as the inspection of natural gas infrastructure that can release methane with much higher concentrations.