We report the first evidence for a nonzero beam-spin azimuthal asymmetry in the electroproduction of positive pions in the deep-inelastic kinematic region. Data for the reaction ep-->e'pi(+)X have been obtained using a polarized electron beam of 4.3 GeV with the CEBAF Large Acceptance Spectrometer at the Thomas Jefferson National Accelerator Facility. The amplitude of the sin phi modulation increases with the momentum of the pion relative to the virtual photon, z. In the range z=0.5-0.8 the average amplitude is 0.038+/-0.005+/-0.003 for a missing mass M-X>1.1 GeV and 0.037+/-0.007+/-0.004 for M-X>1.4 GeV.
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