  We present the first high resolution X-ray image of the dwarf elliptical
galaxy NGC 3226. The data were obtained during an observation of the nearby
Seyfert Galaxy NGC 3227 using the Chandra X-ray Observatory. We detect a point
X-ray source spatially consistent with the optical nucleus of NGC 3226 and a
recently-detected, compact, flat-spectrum, radio source. The X-ray spectrum can
be measured up to ~10 keV and is consistent with a power law with a photon
index 1.7 <~ Gamma <~ 2.2, or thermal bremmstrahlung emission with 4 <~ kT <~
10 keV. In both cases the luminosity in the 2--10 keV band ~10^{40} h_{75}^{-1}
erg/s. We find marginal evidence that the nucleus varies within the
observation. These characteristics support evidence from other wavebands that
NGC 3226 harbors a low-luminosity, active nucleus. We also comment on two
previously-unknown, fainter X-ray sources <~ 15 arcsec from the nucleus of NGC
3226. Their proximity to the nucleus (with projected distances <~ 1.3/h_{75}
kpc) suggests both are within NGC 3226, and thus have luminosities (~few x
10^{38} -- few x 10^{39} erg/s) consistent with black-hole binary systems.
