On April 20, 2010, a cement seal on an oil well operated by British Petroleum in the Gulf of Mexico failed. That resulted in an explosion that killed 11 rig workers and caused the worst environmental disaster in US history and the largest accidental marine oil spill in the history of the petroleum industry. Tens of thousands of claims and lawsuits were filed in American courts by victims of the disaster for personal injuries, damage to property, and loss of business profits. The lawsuits were assigned to the US District Court in New Orleans, Louisiana. Through a combination of maritime, statutory, and common law, that court resolved most of the disputed issues in a little more than two years. Creative procedural approaches, including segmented trials and careful case management, were utilized. A settlement was achieved towards the end of the process that established elaborate court-supervised claims procedures and the use of geographic zones and formulae for determining individual losses. These procedures could be instructive for resolving future mass oil spill disasters. This chapter considers the compensation claims that have arisen from the oil spill disaster caused by the well blowout suffered at the Montara Wellhead Platform in 2009. The chapter is in three substantive sections. Section 2 summarizes the background to the Montara Oil Spill. Section 3 outlines the bases of Australia's and the well operator's potential liability to pay compensation for loss caused by the Montara Oil Spill. Section 4 discusses the challenges likely to be encountered by claimants for compensation. Two related difficulties faced by people seeking compensation for loss suffered following a transboundary oil spill are identified. First is the difficulty of proving that the oil spill caused their loss. Second is the difficulty of proving the extent of loss caused by the oil spill. Nevertheless, private compensation claims under municipal law evidence an emerging facet of potential liability of the oil and gas industry for transboundary pollution.