What would be the effect of CO2 pricing on global oil supply and demand? This paper introduces a model describing the interaction between conventional and non-conventional oil supply in a Hotelling framework and under CO2 constraints. The model assumes that nonconventional crude oil enters the market when conventional oil supply alone is unable to meet demand, and the social cost of CO2 is included in the calculation of the oil rent at that time. The results reveal the effect of a CO2 tax set at the social cost of CO2 on oil price and demand and the uncertainty associated with the time when conventional oil production might become unable to meet demand. The results show that a tax on CO2 emissions associated with fuel use would reduce oil demand despite the effect of lower future rents, and would delay the time when conventional oil supply is unable to satisfy demand. More precisely, between 81 and 99% of the CO2 tax is carried into the oil price despite the counter-balancing effect of the reduced rent. A CO2 tax on fuel use set at the social cost of CO2 would delay by 25 years the time when conventional oil production is unable to meet oil demand, from 2019 to 2044 (mean value). The results show that this date is very sensitive to the price elasticity of demand and the demand growth rate, which shows the great potential of demand-side measures to smooth the transition towards low-carbon liquid fuel alternatives.