  A single-spin asymmetry in the azimuthal distribution of neutral pions
relative to the lepton scattering plane has been measured for the first time in
deep-inelastic scattering of positrons off longitudinally polarized protons.
The analysing power in the sin(phi) moment of the cross section is 0.019 +/-
0.007(stat.) +/- 0.003(syst.). This result is compared to single-spin
asymmetries for charged pion production measured in the same kinematic range.
The pi^0 asymmetry is of the same size as the pi^+ asymmetry and shows a
similar dependence on the relevant kinematic variables. The asymmetry is
described by a phenomenological calculation based on a fragmentation function
that represents sensitivity to the transverse polarization of the struck quark.
