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(ox) values, Delta alpha(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(eff) = 0.5(-0.4)(+0.5). These findings support the presence of heavy X-ray absorption (N-H approximate to 2 x 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.