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 concentrations^2,3; however, the magnitude of this increase is uncertain. Atmospheric chemistry models typically predict^4,5,6,7 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 cent^8,9,10 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 O₂decreased 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 precursors^4,5,11. 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.