  We determine the total enclosed mass profile from 0.7 to 35 kpc in the
elliptical galaxy NGC 4636 based on the hot interstellar medium temperature
profile measured using the Chandra X-ray Observatory, and other X-ray and
optical data. The total mass increases as radius to the power 1.2 to a good
approximation over this range in radii, attaining a total mass-to-light ratio
of 40 solar masses per solar visual luminosity at 35 kpc. We find that at least
half, and as much as 80%, of the mass within the optical half-light radius is
non-luminous, implying an exceptionally low baryon fraction in NGC 4636. The
large inferred dark matter concentration and central dark matter density,
consistent with the upper end of the range expected for standard cold dark
matter halos, imply that mechanisms proposed to explain low dark matter
densities in less massive galaxies are not effective in elliptical galaxies.
