We present $Chandra$ observations of seven broad absorption line (BAL) quasars at $z=0.863$-2.516 with redshifted BAL troughs (RSBALs). Five of our seven targets were detected by $Chandra$ in 4-13 ks exposures with ACIS-S. The $alpha_{rm ox}$ values, $Deltaalpha_{rm ox}$ values, and spectral energy distributions of our targets demonstrate they are all X-ray weak relative to expectations for non-BAL quasars, and the degree of X-ray weakness is consistent with that of appropriately-matched BAL quasars generally. Furthermore, our five detected targets show evidence for hard X-ray spectral shapes with a stacked effective power-law photon index of $Gamma_{rm eff}=0.5^{+0.5}_{-0.4}$. These findings support the presence of heavy X-ray absorption ($N_{rm H}approx 2 times 10^{23}$ cm$^{-2}$) in RSBAL quasars, likely by the shielding gas found to be common in BAL quasars more generally. We use these X-ray measurements to assess models for the nature of RSBAL quasars, finding that a rotationally-dominated outflow model is favored while an infall model also remains plausible with some stipulations. The X-ray data disfavor a binary quasar model for RSBAL quasars in general.
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