A new method of measuring angular diameter distances, and hence H0 and q0, by means of X-ray observations of galaxy clusters is proposed. It resembles the method which combines maps of X-ray continuum emission with maps of the Suniaev-Zel'dovich effect, but substitutes measurements of X-ray absorption lines in the spectra of background quasars for the Suniaev-Zel'dovich effect. When the high resolution permitted by the AXAF microcalorimeter becomes available, this method should yield results with significantly smaller uncertainty.