We present Chandra observations of 12 galaxies that contain supermassive black holes with dynamical mass measurements. Each galaxy was observed for 30 ksec and resulted in a total of 68 point source detections in the target galaxies including supermassive black hole sources, ultraluminous X-ray sources, and extragalactic X-ray binaries. Based on our fits of the X-ray spectra, we report fluxes, luminosities, Eddington ratios, and slope of the power-law spectrum. Normalized to the Eddington luminosity, the 2--10 keV band X-ray luminosities of the SMBH sources range from $10^{-8}$ to $10^{-6}$, and the power-law slopes are centered at $∼2$ with a slight trend towards steeper (softer) slopes at smaller Eddington fractions, implying a change in the physical processes responsible for their emission at low accretion rates. We find 20 ULX candidates, of which six are likely ($>90%$ chance) to be true ULXs. The most promising ULX candidate has an isotropic luminosity in the 0.3--10 keV band of $1.0_{-0.3}^{+0.6} \times 10^{40}$ erg/s. ; Comment: Accepted by ApJ. 16 pages, 8 figures, 5 tables