The atmospheric chemistry of volatile organic compounds (VOCs) in urban areas results in the formation of 'photochemical smog', including secondary organic aerosol (SOA). State-of-the-art SOA models parameterize the results of simulation chamber experiments that bracket the conditions found in the polluted urban atmosphere. Here we show that in the real urban atmosphere reactive anthropogenic VOCs (AVOCs) produce much larger amounts of SOA than these models predict, even shortly after sunrise. Contrary to current belief, a significant fraction of the excess SOA is formed from first-generation AVOC oxidation products. Global models deem AVOCs a very minor contributor to SOA compared to biogenic VOCs (BVOCs). If our results are extrapolated to other urban areas, AVOCs could be responsible for additional 3--25 Tg yr-1 SOA production globally, and cause up to -0.1 W m-2 additional top-of-the-atmosphere radiative cooling.