  A first measurement is reported of the longitudinal proton structure function
F_L(x,Q^2) at the ep collider HERA. It is based on inclusive deep inelastic
e^+p scattering cross section measurements with a positron beam energy of 27.5
GeV and proton beam energies of 920, 575 and 460 GeV. Employing the energy
dependence of the cross section, F_L is measured in a range of squared
four-momentum transfers 12 < Q^2 < 90 GeV^2 and low Bjorken x 0.00024 < x <
0.0036. The F_L values agree with higher order QCD calculations based on parton
densities obtained using cross section data previously measured at HERA.
