Tropospheric ozone (O3) is a key component of air pollution and an important anthropogenic greenhouse gas1. During the twentieth century, the proliferation of the internal combustion engine, rapid industrialization and land-use change led to a global-scale increase in O3 concentrations2,3; however, the magnitude of this increase is uncertain. Atmospheric chemistry models typically predict4–7 an increase in the tropospheric O3 burden of between 25 and 50 per cent since 1900, whereas direct measurements made in the late nineteenth century indicate that surface O3 mixing ratios increased by up to 300 per cent8–10 over that time period. However, the accuracy and diagnostic power of these measurements remains controversial2. Here we use a record of the clumped-isotope composition of molecular oxygen (18O18O in O2) trapped in polar firn and ice from 1590 to 2016 ad, as well as atmospheric chemistry model simulations, to constrain changes in tropospheric O3 concentrations. We find that during the second half of the twentieth century, the proportion of 18O18O in O2 decreased by 0.03 ± 0.02 parts per thousand (95 per cent confidence interval) below its 1590–1958 ad mean, which implies that tropospheric O3 increased by less than 40 per cent during that time. These results corroborate model predictions of global-scale increases in surface pollution and vegetative stress caused by increasing anthropogenic emissions of O3 precursors4,5,11. We also estimate that the radiative forcing of tropospheric O3 since 1850 ad is probably less than +0.4 watts per square metre, consistent with results from recent climate modelling studies12. © 2019, The Author(s), under exclusive licence to Springer Nature Limited.