We study how carbon prices affect labor market outcomes by exploiting a policy change in the EU Emissions Trading System that led to a sharp rise in permit prices. Using population-wide employer-employee matched data from the Netherlands and a matched difference-in-differences design, we find no adverse aggregate effects on employment or wages. However, the distributional effects are sizable: workers in firms with large permit surpluses experience wage gains, as do STEM-educated workers---especially those with stronger outside options. Plants employing more STEM workers achieve larger reductions in energy costs, highlighting the role of skills in facilitating the transition to low-carbon technologies. Our results illustrate that distributional effects of carbon pricing depend on market design and worker skills.