Although mainly used for other purposes, and historically mainly established at the expense of tropical forests, oil palm can be the most land efficient feedstock for biodiesel. Large parts of Brazil are suitable for oil palm cultivation and a series of policy initiatives have recently been launched to promote oil palm production. These initiatives are however highly debated both in the parliament and in academia. Here we present results of a high resolution modelling study of opportunities and risks associated with oil palm production for biodiesel in Brazil, under different energy, policy, and infrastructure scenarios. Oil palm was found to be profitable on extensive areas, including areas under native vegetation where establishment would cause large land use change (LUC) emissions. However, some 40-60 Mha could support profitable biodiesel production corresponding to approximately 10% of the global diesel demand, without causing direct LUC emissions or impinging on protected areas. Pricing of LUC emissions could make oil palm production unprofitable on most lands where conversion would impact on native ecosystems and carbon stocks, if the carbon price is at the level $125/tC, or higher.