This paper identifies combinations of technical and behavioral measures that lead to progressively lower global demand for oil, culminating with a scenario that eliminates global oil demand by 2060-in line with the broader requirement that anthropogenic CO2 emissions reach net zero by this date in order to have a 60% chance of staying below a global mean warming of 2 degrees C above the pre-industrial level. The cumulative oil consumption from 2010 to the point when zero oil demand is achieved is compared with a recent oil supply-marginal cost curve. Assuming that oil is consumed in order of increasing extraction cost, the price of oil need not rise significantly above $25-35/bbl. Even substantially less-aggressive efforts to reduce CO2 emissions need not see oil rise substantially above $50/bbl. Under aggressive climate policies, the peak in oil demand occurs before the supply-constrained peak in oil production would occur. This would render expensive oil (> $50/bbl) permanently uneconomic. This includes oil from the Canadian tar sands (currently costing $65-95/bbl for new greenfield developments) and most shale oil (with current average oil-play costs of $48-65/bbl). This in turn implies that governments should not be promoting or permitting development of high cost oil, and also provides a clear warning to private and institutional investors.