The spin asymmetryAN for inclusive π0 production by 200-GeV transversely-polarized protons on a liquid hydrogen target has been measured at Fermilab over a wide range ofxF, with 0.5<pT<2 GeV/c. AtxF>0.3, the asymmetry rises with increasingxF and reaches a value ofAN=0.15±0.03 in the region 0.6<xF<0.8. This result provides new input regarding the question of the internal spin structure of transversely-polarized protons.