The spectacular "first light" observation by the Chandra X-Ray Observatory revealed an X-ray point source near the center of the 300 yr old Cas A supernova remnant. We present an analysis of the public X-ray spectral and timing data. No coherent pulsations were detected in the Chandra/HRC data. The 3 σ upper limit on the pulsed fraction is less than 35% for P > 20 ms. The Chandra/ACIS spectrum of the point source may be fitted with an ideal blackbody (kT = 0.5 keV) or with blackbody models modified by the presence of a neutron star atmosphere (kT = 0.25-0.35 keV), but the temperature is higher and the inferred emitting area lower than expected for a 300 yr old neutron star according to standard cooling models. The spectrum may also be fitted with a power-law model (photon index Γ = 2.8-3.6). Both the spectral properties and the timing limits of the point source are inconsistent with a young Crab-like pulsar but are quite similar to the properties of the anomalous X-ray pulsars. The spectral parameters are also very similar to those of the other radio-quiet X-ray point sources in the supernova remnants Pup A, RCW 103, and PKS 1209-52. Current limits on an optical counterpart for the Cas A point source rule out models that invoke fallback accretion onto a compact object if fallback disk properties are similar to those in quiescent low-mass X-ray binaries. However, the optical limits are marginally consistent with plausible alternative assumptions for a fallback disk. In this case, accreting neutron star models can explain the X-ray data, but an accreting black hole model is not promising.