  A measurement of the beam-spin asymmetry in the azimuthal distribution of
pions produced in semi-inclusive deep-inelastic scattering off protons is
presented. The measurement was performed using the {HERMES} spectrometer with a
hydrogen gas target and the longitudinally polarized 27.6 GeV positron beam of
HERA. The sinusoidal amplitude of the dependence of the asymmetry on the angle
$\phi$ of the hadron production plane around the virtual photon direction
relative to the lepton scattering plane was measured for $\pi^+,\pi^-$ and
$\pi^0$ mesons. The dependence of this amplitude on the Bjorken scaling
variable and on the pion fractional energy and transverse momentum is
presented. The results are compared to theoretical model calculations.
