Utilizing Chandra X-ray observations in the All-wavelength Extended Groth Strip International Survey (AEGIS) we identify 241 X-ray selected Active Galactic Nuclei (AGNs, L > 10^{42} ergs/s) and study the properties of their host galaxies in the range 0.4 < z < 1.4. By making use of infrared photometry from Palomar Observatory and BRI imaging from the Canada-France-Hawaii Telescope, we estimate AGN host galaxy stellar masses and show that both stellar mass and photometric redshift estimates (where necessary) are robust to the possible contamination from AGNs in our X-ray selected sample. Accounting for the photometric and X-ray sensitivity limits of the survey, we construct the stellar mass function of X-ray selected AGN host galaxies and find that their abundance decreases by a factor of ~2 since z~1, but remains roughly flat as a function of stellar mass. We compare the abundance of AGN hosts to the rate of star formation quenching observed in the total galaxy population. If the timescale for X-ray detectable AGN activity is roughly 0.5-1 Gyr--as suggested by black hole demographics and recent simulations--then we deduce that the inferred AGN trigger rate matches the star formation quenching rate, suggesting a link between these phenomena. However, given the large range of nuclear accretion rates we infer for the most massive and red hosts, X-ray selected AGNs may not be directly responsible for quenching star formation.