I consider the thermal bremsstrahlung emission from hot accretion flows (Bondi/ADAFs), taking into account the finite size of the observing telescope's beam (R_beam) relative to the Bondi accretion radius (R_A). For R_beam >> R_A soft X-ray emission from the hot interstellar medium surrounding the black hole dominates the observed emission while for R_beam << R_A hard X-ray emission from the accretion flow dominates. I apply these models to Chandra observations of the Galactic Center, for which

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... R_beam ~ R_A. I argue that bremsstrahlung emission accounts for most of the "quiescent" (non-flaring) flux observed by Chandra from Sgr A*; this emission is spatially extended on scales ~ R_A ~ 1" and has a relatively soft spectrum, as is observed. If accretion onto the central black hole proceeds via a Bondi or ADAF flow, a hard X-ray power law should be present in deeper observations with a flux ~ 1/3 of the soft X-ray flux; nondetection of this hard X-ray component would argue against ADAF/Bondi models. I briefly discuss the application of these results to other low-luminosity AGN.