Gas undergoing Bondi accretion onto a supermassive black hole (SMBH) becomes hotter toward smaller radii. We searched for this signature with a Chandra observation of the hot gas in NGC 3115, which optical observations show has a very massive SMBH. Our analysis suggests that we are resolving, for the first time, the accretion flow within the Bondi radius of an SMBH. We show that the temperature is rising toward the galaxy center as expected in all accretion models in which the black hole is gravitationally capturing the ambient gas. There is no hard central point source that could cause such an apparent rise in temperature. The data support that the Bondi radius is at about 4 arcsec-5 arcsec (188-235 pc), suggesting an SMBH of 2 x 10^9 M_sun that is consistent with the upper end of the optical results. The density profile within the Bondi radius has a power-law index of 1.03^{+0.23}_{-0.21} which is consistent with gas in transition from the ambient medium and the accretion flow. The accretion rate at the Bondi radius is determined to be {dot M}_B = 2.2 x 10^{-2} M_sun yr^{-1}. Thus, the accretion luminosity with 10% radiative efficiency at the Bondi radius (10^{44} erg s^{-1}) is about six orders of magnitude higher than the upper limit of the X-ray luminosity of the nucleus.
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