A measurement of the proton spin structure function g1p(x,Q^2) in
deep-inelastic scattering is presented. The data were taken with the 27.6 GeV
longitudinally polarised positron beam at HERA incident on a longitudinally
polarised pure hydrogen gas target internal to the storage ring. The kinematic
range is 0.021<x<0.85 and 0.8 GeV^2<Q^2<20 GeV^2. The integral
Int_{0.021}^{0.85} g1p(x)dx evaluated at Q0^2 of 2.5 GeV^2 is
0.122+/-0.003(stat.)+/-0.010(syst.).Comment: 7 pages, 3 figures, 1 table, RevTeX late