We present the results of a 100 ks {it Chandra} observation of the NGC 404 nuclear region. The long exposure and excellent spatial resolution of {it Chandra} has enabled us to critically examine the nuclear environment of NGC 404, which is known to host a nuclear star cluster and potentially an intermediate-mass black hole (on the order of a few times $10^5$ Msun). We find two distinct X-ray sources: a hard, central point source coincident with the optical and radio centers of the galaxy, and a soft extended region that is coincident with areas of high H$alpha$ emission and likely recent star formation. When we fit the 0.3-8 keV spectra of each region separately, we find the hard nuclear point source to be dominated by a power law (PL = 1.88), while the soft off-nuclear region is best fit by a thermal plasma model ($kT$ = 0.67 keV). We therefore find evidence for both a power law component and hot gas in the nuclear region of NGC 404. We estimate the 2-10 keV luminosity to be 1.3$^{+0.8}_{-0.5}times10^{37}$ erg s$^{-1}$. A low-level of diffuse X-ray emission is detected out to $sim$15as ($sim$0.2 kpc) from the nucleus. We compare our results to the observed relationships between power law photon index and Eddington ratio for both X-ray binaries and low luminosity active galaxies and find NGC 404 to be consistent with other low luminosity active galaxies. We therefore favor the conclusion that NGC 404 harbors an intermediate-mass black hole accreting at a very low level.
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