We have observed three quasars, PKS 1127-145, Q 1331+171 and Q0054+144, with the ACIS-S aboard the Chandra X-ray Observatory, in order to measure soft X-ray absorption associated with intervening 21-cm and damped Ly$alpha$ absorbers. For PKS 1127-145, we detect absorption which, if associated with an intervening z_{abs}=0.312 absorber, implies a metallicity of 23% solar. If the absorption is not at z_{abs}=0.312, then the metallicity is still constrained to be less than 23% solar. The advantage of the X-ray measurement is that the derived metallicity is insensitive to ionization, inclusion of an atom in a molecule, or depletion onto grains. The X-ray absorption is mostly due to oxygen, and is consistent with the oxygen abundance of 30% solar derived from optical nebular emission lines in a foreground galaxy at the redshift of the absorber. For Q1331+171 and Q 0054+144, only upper limits were obtained, although the exposure times were intentionally short, since for these two objects we were interested primarily in measuring flux levels to plan for future observations. The imaging results are presented in a companion paper.