We present deep (250 ks) Chandra observations of the nearby galaxy group NGC 1600, which has at its center an ultramassive black hole (17 billion solar masses). The exceptionally large mass of the black hole coupled with its low redshift makes it one of only a handful of black holes for which spatially resolved temperature and density profiles can be obtained within the Bondi radius with the high spatial resolution of Chandra. We analyzed the hot gas properties within the Bondi accretion radius. Within a ~3 kpc radius, we find two temperature components. Both the single-temperature and two-temperature models show only a very slight rise in temperature towards the center, and are consistent with being flat. This is in contrast with the expectation from Bondi accretion for a temperature profile which increases towards the center, and appears to indicate that the dynamics of the gas are not being determined by the central black hole. The density profile follows a relatively shallow relationship within the Bondi radius, which suggests that the true accretion rate on to the black hole may be lower than the classical Bondi accretion rate.