In this paper, a measurement of τ polarization in W → τν decays is presented. It is measured from the energies of the decay products in hadronic τ decays with a single final state charged particle. The data, corresponding to an integrated luminosity of 24 pb−1, were collected by the ATLAS experiment at the Large Hadron Collider in 2010. The measured value of the τ polarization is Pτ = −1.06±0.04 (stat) +0.05−0.07 (syst), in agreement with the Standard Model prediction, and is consistent with a physically allowed 95 % CL interval [−1,−0.91]. Measurements of τ polarization have not previously been made at hadron colliders.