The first search for supersymmetry in events with an experimental signature of one soft, hadronically decaying τ lepton, one energetic jet from initial-state radiation, and large transverse momentum imbalance is presented. These event signatures are consistent with direct or indirect production of scalar τ leptons (˜τ) in supersymmetric models that exhibit coannihilation between the ˜τ and the lightest neutralino (˜χ01), and that could generate the observed relic density of dark matter. The data correspond to an integrated luminosity of 77.2  fb−1 of proton-proton collisions at √s=13  TeV collected with the CMS detector at the LHC in 2016 and 2017. The results are interpreted in a supersymmetric scenario with a small mass difference (Δm) between the chargino (˜χ±1) or next-to-lightest neutralino (˜χ02), and the ˜χ01. The mass of the ˜τ is assumed to be the average of the ˜χ±1 and ˜χ01 masses. The data are consistent with standard model background predictions. Upper limits at 95% confidence level are set on the sum of the ˜χ±1, ˜χ02, and ˜τ production cross sections for Δm(˜χ±1,˜χ01)=50  GeV, resulting in a lower limit of 290 GeV on the mass of the ˜χ±1, which is the most stringent to date and surpasses the bounds from the LEP experiments.