(Abridged) We present a deep Chandra observation of the late-type barred spiral galaxy NGC 2903. The Chandra data reveal soft (kT_e ~ 0.2-0.5keV) diffuse emission in the nuclear starburst region and extending ~5kpc to the north and west of the nucleus. Much of this soft hot gas is likely to be from local active star-forming regions; however, besides the nuclear region, the morphology of hot gas does not strongly correlate with sites of active star formation. The central ~650 pc radius starburst zone exhibits much higher surface brightness diffuse emission than the surrounding regions and a harder spectral component in addition to its soft component. We interpret the hard component as being of thermal origin with kT_e~3.6keV and to be directly associated with a wind fluid produced by supernovae and massive star winds. The inferred terminal velocity for this hard component, ~1100 km/s, exceeds the local galaxy escape velocity suggesting a potential outflow. The softer extended emission does not display an obvious outflow geometry. However, the column density through which the X-rays are transmitted is lower to the west of the nucleus compared to the east and the surface brightness is higher there suggesting some soft hot gas originates from above the disk; viewed directly from the western zone but through the intervening galaxy disk from the eastern zone. There are several point-like sources in the nuclear region with X-ray spectra typical of compact binaries. None of these are coincident with the mass center of the galaxy and we place an upper limit luminosity from any point-like nuclear source to be < 2x10^38 ergs/s in the 0.5-8.0keV band which indicates that NGC 2903 lacks an active galactic nucleus. Heating from the nuclear starburst and a galactic wind may be responsible for preventing cold gas from accreting onto the galactic center.
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