The first measurement of the CP structure of the Yukawa coupling between the Higgs boson and τ leptons is presented. The measurement is based on data collected in proton-proton collisions at s = 13 TeV by the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb−1. The analysis uses the angular correlation between the decay planes of τ leptons produced in Higgs boson decays. The effective mixing angle between CP-even and CP-odd τ Yukawa couplings is found to be −1 ± 19°, compared to an expected value of 0 ± 21° at the 68.3% confidence level. The data disfavour the pure CP-odd scenario at 3.0 standard deviations. The results are compatible with predictions for the standard model Higgs boson. [Figure not available: see fulltext.]