Oil and natural gas wells are a prominent source of the greenhouse gas methane (CH4), but most measurements are from newer, high producing wells. There are nearly 700,000 marginal "stripper" wells in the US, which produce less than 15 barrels of oil equivalent (BOE) d-1. We made direct measurements of CH4 and volatile organic carbon (VOC) emissions from marginal oil and gas wells in the Appalachian Basin of southeastern Ohio, all producing < 1 BOE d-1. Methane and VOC emissions followed a skewed distribution, with many wells having zero or low emissions and a few wells responsible for the majority of emissions. The average CH4 emission rate from marginal wells was 128 g h-1 (median: 18 g h-1; range: 0- 907 g h-1). Follow-up measurements at five wells indicated high emissions were not episodic. Some wells were emitting all or more of the reported gas produced at each well, or venting gas from wells with no reported gas production. Measurements were made from wellheads only, not tanks, so our estimates may be conservative. Stochastic processes such as maintenance may be the main driver of emissions. Marginal wells are a disproportionate source of CH4 and VOCs relative to oil and gas production. We estimate that oil and gas wells in this lowest production category emit approximately 11% of total annual CH4 from oil and gas production in the EPA greenhouse gas inventory, although they produce about 0.2% of oil and 0.4% of gas in the US per year. Implications: Low producing marginal wells are the most abundant type of oil and gas well in the United States, and a surprising number of them are venting all or more of their reported produced gas to the atmosphere. This makes marginal wells a disproportionate greenhouse gas emissions source compared to their energy return, and a good target for environmental mitigation.