The transfer of polarization from a high-energy positron to a Λ0 hyperon produced in semiinclusive deep-inelastic scattering has been measured. The data have been obtained by the HERMES experiment at DESY using the 27.6 GeV longitudinally polarized positron beam of the HERA collider and unpolarized gas targets internal to the positron (electron) storage ring. The longitudinal spin-transfer coefficient is found to be DLL′Λ=0.11±0. 10(stat)±0.03(syst) at an average fractional energy carried by the Λ0 hyperon z=0.45. The dependence of DLL′Λ on both the fractional energy z and the fractional longitudinal momentum xF is presented. © 2006 The American Physical Society.