Abstract The Lyα luminosity function (LF) of Lyα emitters (LAEs) has been used to constrain the neutral hydrogen fraction in the intergalactic medium (IGM) and thus the timeline of cosmic reionization. Here we present the results of a new narrowband imaging survey for z = 7.3 LAEs in a large area of ∼3 deg² with Subaru/Hyper Suprime-Cam. No LAEs are detected down to L _Lyα ≃ 10^43.2 erg s⁻¹ in an effective cosmic volume of ∼2 × 10⁶ Mpc³, placing an upper limit on the bright part of the z = 7.3 Lyα LF for the first time and confirming a decrease in bright LAEs from z = 7.0. By comparing this upper limit with the Lyα LF in the case of fully ionized IGM, which is predicted using an observed z = 5.7 Lyα LF on the assumption that the intrinsic Lyα LF evolves in the same way as the UV LF, we obtain the relative IGM transmission T Ly α IGM ( 7.3 ) / T Ly α IGM ( 5.7 ) < 0.77 and then the volume-averaged neutral fraction x _{H I}(7.3) > 0.28. Cosmic reionization is thus still ongoing at z = 7.3, consistent with results from other x _{H I} estimation methods. A similar analysis using literature Lyα LFs finds that at z = 6.6 and 7.0, the observed Lyα LF agrees with the predicted one, consistent with full ionization.