Oil palm is a land efficient feedstock alternative for biodiesel production and can be a very profitable alternative for farmers. In this study, a spatially explicit model is used to: (i) map and quantify areas in Brazil where oil palm establishment for biodiesel production would be profitable (positive net present value, NPV) in different future scenarios; (ii) estimate corresponding biodiesel production volumes and analyze trade-offs between such biodiesel production, greenhouse gas emissions reduction, and nature conservation; and (iii) investigate whether pricing of carbon emissions from land use change might help to steer oil palm production away from lands where conversion would bring the largest impacts on biodiversity or ecosystem carbon stocks. The scenarios include oil, coal, and carbon price pathways from the IEA World Energy Outlook and both the present and prospective situations concerning road infrastructure in Brazil. It is found that palm oil production for biodiesel can be profitable (positive NPV) on very large areas; that such production can conflict with greenhouse gas emissions reduction and nature conservation objectives in many places, but also provide opportunities to meet multiple objectives. Depending on scenario, some 65-80 Mha of land could support biodiesel production corresponding to more than 10% of the global diesel demand, without causing any direct land use change emissions and without inflicting on high conservation value areas.