A number of international donors, national governments and project proponents have begun to lay the groundwork for REDD+, but tenure insecurity - including the potential risks of land grabbing by outsiders and loss of local user rights to forests and forest land - is one of the main reasons that many indigenous and other local peoples have publicly opposed it. Under what conditions is REDD+ a threat to local rights, and under what conditions does it present an opportunity? This article explores these issues based on available data from a global comparative study on REDD+, led by the Center for International Forestry Research, which is studying national policies and processes in 12 countries and 23 REDD+ projects in 6 countries. The article analyses how tenure concerns are being addressed at both national and project level in emerging REDD+ programs. The findings suggest that in most cases REDD+ has clearly provided some new opportunities for securing local tenure rights, but that piecemeal interventions by project proponents at the local level are insufficient in the absence of broader, national programs for land tenure reform. The potential for substantial changes in the status quo appear unlikely, though Brazil - the only one with such a national land tenure reform program - offers useful insights. Land tenure reform - the recognition of customary rights in particular - and a serious commitment to REDD+ both challenge the deep-rooted economic and political interests of 'business as usual'.