In this paper, we assess a new feature of carbon taxes in small open economies specializing in the export of a single commodity. This is, the ability to reduce the volatility of the real exchange rate in the Chilean economy. This is done trough the lens of a DSGE model that features an externality that affects the economy GDP. This originates from the burning process of fossil fuels, used for energy generation. We assume that this externality is the driver of climate change and that the government, seeking to internalize these damages, levies a Pigouvian tax in the energy sector. A key aspect of the tax is that it is optimal, as it accounts for the social cost of carbon. Under further assumptions, it can be expressed as a fraction of GDP, depending only on exogenous parameters: the carbon cycle depreciation structure parameters, the expected damages in GDP and the discount factor. The results shows that the tax: (i) cuts emissions by roughly 8% and increases the energy price by 11%, (ii) is a welfare improving policy and finally, (iii) reduces the real exchange rate variance by 1.8%. The stabilization of this variable is robust to the shock specification under assessment. In effect, when the economy is exposed to single and multiple copper price shocks, or multiple mixed shocks, the carbon tax helps to reduce the real exchange rate volatility by an amount ranging between 1.8% and 2.2%.