The production of leading neutrons, where the neutron carries a large fraction xL of the incoming proton's longitudinal momentum, is studied in deep-inelastic positron-proton scattering at HERA. The data were taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 122 pb-1. The semi-inclusive cross section is measured in the phase space defined by the photon virtuality 6<Q2<100 GeV2, Bjorken scaling variable 1.5{dot operator}10-4< x <3{dot operator}10-2, longitudinal momentum fraction 0. 32<xL<0.95 and neutron transverse momentum pT<0.2 GeV. The leading neutron structure function, FLN(3)2(Q2,x, xL), and the fraction of deep-inelastic scattering events containing a leading neutron are studied as a function of Q2, x and xL. Assuming that the pion exchange mechanism dominates leading neutron production, the data provide constraints on the shape of the pion structure function. © 2010 The Author(s).