We analyze a dynamic stochastic general equilibrium model which includes a negative externality that arises from fossil fuels burning. The carbon released to the atmosphere by electricity producers is the main driver of climate change. We adapt the optimal tax derived by Golosov et al. (2011) to a small open economy to force polluters to internalize their damages. The results show that the tax benefits outweigh their costs; yet welfare gains seem to be marginal under plausible parameters. We calculate the optimal carbon tax for Chile and the tax effectiveness achieved, which is around 10 percent. The results remain robust to variations in the utility function, changes in parameters that determine the externality and alternative degrees of commitment to reduce emissions.