The proliferation of unconventional natural gas drilling has brought considerable recent attention to the possible impacts that this new technology may have on greenhouse gas emissions. In Pennsylvania, estimates of these possible impacts are very difficult to accurately assess in large part due to the highly uncertain contribution from legacy abandoned and orphaned gas (AOG) wells. This paper outlines our work in establishing a methodology for measuring the methane leak rate from AOG wells in Western Pennsylvania. The theory and methodology of an enclosure method for measuring the methane mass leak rate from one AOG natural gas well is described. Summary data for four other measurements and three other wells is presented. The goal of this work is to take the first steps towards an accurate determination of the contribution of AOWs to anthropogenic methane emissions in Pennsylvania.