Papua New Guinea (PNG) has become the focus of climate change mitigation initiatives such as reducing emissions from deforestation and forest degradation, but defensible estimates of forest carbon are lacking. Here we present a methodology for estimating aboveground forest carbon, and apply it to a large Permanent Sample Plot system maintained by Papua New Guinea Forest Research Institute. We report the first estimates of forest carbon in lowland tropical forest in PNG. Average aboveground carbon in stems >10 cm diam. for 115 selectively harvested 1-ha plots in lowland tropical forest was 66.3±3.5 Mg C/ha (95% CI) while for 10 primary forest plots the average was 106.3±16.2 Mg C/ha. We applied ratios based on field observations, in-country studies, and the literature to estimate unmeasured pools of aboveground carbon (stems <10 cm diam., fine litter and coarse woody debris). Total aboveground carbon was estimated at 90.2 and 120.8 Mg C/ha in selectively harvested and primary lowland forest, respectively. Our estimate for primary tropical forest is lower than biome averages for tropical equatorial forest, and we hypothesize that frequent disturbances from fire, frost, landslides, and agriculture are limiting carbon stock development. The methodology and estimates presented here will assist the PNG government in its preparedness for mitigation initiatives, are of interest to communities that are seeking to participate in voluntary carbon markets, and will encourage transparency and consistency in the estimation of forest carbon.