The double helicity asymmetry in neutral pion production for p{sub T}=1 to 12 GeV/c was measured with the PHENIX experiment to access the gluon-spin contribution, DELTAG, to the proton spin. Measured asymmetries are consistent with zero, and at a theory scale of mu{sup 2}=4 GeV{sup 2} a next to leading order QCD analysis gives DELTAG{sup 0.02,0.3}=0.2, with a constraint of -0.7<DELTAG{sup 0.02,0.3}<0.5 at DELTAchi{sup 2}=9 (approx3sigma) for the sampled gluon momentum fraction (x) range, 0.02 to 0.3. The results are obtained using predictions for the measured asymmetries generated from four representative fits to polarized deep inelastic scattering data. We also consider the dependence of the DELTAG constraint on the choice of the theoretical scale, a dominant uncertainty in these predictions.