We present a microlensing analysis of 61 Chandra observations of 14 quadruply lensed quasars. X-ray flux measurements of the individual quasar images give a clean determination of the microlensing effects in the lensing galaxy and thus offer a direct assessment of the local fraction of stellar matter making up the total integrated mass along the lines of sight through the lensing galaxy. A Bayesian analysis of the ensemble of lensing galaxies gives a most likely local stellar fraction of 7%, with the other 93% in a smooth, dark matter component, at an average impact parameter R_c of 6.6 kpc from the center of the lensing galaxy. We divide the systems into smaller ensembles based on R_c and find that the most likely local stellar fraction varies qualitatively and quantitatively as expected, decreasing as a function of R_c.