Lyman- and Werner-band absorption of molecular hydrogen ( H _ { 2 } ) is detected in \sim 50 % of low-redshift ( z < 1 ) DLAs / sub-DLAs with N ( \mbox { H { $ { } _ { 2 } $ } } ) > 10 ^ { 14.4 } cm ^ { -2 } . However , the true origin ( s ) of the H _ { 2 } -bearing gas remain elusive . Here we report a new detection of an H _ { 2 } absorber at z _ { abs } = 0.4298 in the HST / COS spectra of quasar PKS 2128–123 . The total N ( \mbox { H { \sc i } } ) of 10 ^ { 19.50 \pm 0.15 } cm ^ { -2 } classifies the absorber as a sub-DLA . H _ { 2 } absorption is detected up to the J = 3 rotational level with a total \log N ( \mbox { H { $ { } _ { 2 } $ } } ) = 16.36 \pm 0.08 corresponding to a molecular fraction of \log f _ { \mbox { \footnotesize H { $ { } _ { 2 } $ } } } = -2.84 \pm 0.17 . The excitation temperature of T _ { ex } = 206 \pm 6 K indicates the presence of cold gas . Using detailed ionization modeling we obtain a near-solar metallicity ( i.e. , [ O / H ] = -0.26 \pm 0.19 ) and a dust-to-gas ratio of \log \kappa \sim - 0.45 for the H _ { 2 } -absorbing gas . The host galaxy of the sub-DLA is detected at an impact parameter of \rho \sim 48 kpc with an inclination angle of i \sim 48 ^ { \circ } and an azimuthal angle of \Phi \sim 15 ^ { \circ } with respect to the QSO sightline . We show that co-rotating gas in an extended disk can not explain the observed kinematics of Mg ii absorption . Moreover , the inferred high metallicity is not consistent with the scenario of gas accretion . An outflow from the central region of the host galaxy , on the other hand , would require a large opening angle ( i.e. , 2 \theta > 150 ^ { \circ } ) , much larger than the observed outflow opening angles in Seyfert galaxies , in order to intercept the QSO sightline . We thus favor a scenario in which the H _ { 2 } -bearing gas is stemming from a dwarf-satellite galaxy , presumably via tidal and / or ram pressure stripping . Detection of a dwarf galaxy candidate in the HST / WFPC2 image at an impact parameter of \sim 12 kpc reinforces such an idea .