We report the measurement of beam-target double spin asymmetries (A(LT)) in the inclusive production of identified hadrons, (e) over right arrow + 3He(up arrow) -> h + X, using a longitudinally polarized 5.9-GeV electron beam and a transversely polarized He-3 target. Hadrons (pi(+/-), K-+/-, and proton) were detected at 16 degrees with an average momentum < Ph > = 2.35 GeV/c and a transverse momentum (p(T)) coverage from 0.60 to 0.68 GeV/c. Asymmetries from the He-3 target were observed to be nonzero for pi(+/-) production when the target was polarized transversely in the horizontal plane. The pi(+) and pi(-) asymmetries have opposite signs, analogous to the behavior of A(LT) in semi-inclusive deep-inelastic scattering.