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We report the first measurement of the transverse momentum dependence of double-spin asymmetries in semi-inclusive production of pions in deep-inelastic scattering off the longitudinally polarized proton. Data have been obtained using a polarized electron beam of 5.7 GeV with the CLAS detector at the Jefferson Lab (JLab). Modulations of single spin asymmetries over the azimuthal angle between lepton scattering and hadron production planes phi have been measured over a wide kinematic range in Bjorken x and virtual photon squared four-momentum Q(2). A significant nonzero sin2 phi single spin asymmetry was observed for the first time indicating strong spin-orbit correlations for transversely polarized quarks in the longitudinally polarized proton.