The two-spin parameter A LL in inclusive π 0 productionby longitudinally-polarized protons and antiprotons on a longitudinally-polarized proton target has been measured at the 200 GeV Fermilab spin physics facility, for π 0 's at x F =0 with 1⩽ p t ⩽3 GeV/ c . The results exclude, at the 95% confidence level, values of A LL (pp) > 0.1 and < − 0.1 for π 0 's produced by protons, and values of A LL ( p p) > 0.1 and < −0.2 for incident antiprotons. The relevance of A LL (pp) for the gluon spin density is discussed. The data are in good agreement with “conventional”, small or zero, gluon polarization.