We present a detailed analysis of high-resolution Chandra observations of the merger system NGC3256 , the most IR luminous galaxy in the nearby universe . The X-ray data show that several discrete sources embedded in complex diffuse emission contribute \ga 20 \% of the total emission ( L _ { x } ^ { tot } \sim 8 \times 10 ^ { 41 } ergs s ^ { -1 } in the 0.5-10 keV energy range ) . The compact sources are hard and extremely bright and their emission is probably dominated by accretion driven processes . Both galaxy nuclei are detected with L _ { x } \sim 3 - 10 \times 10 ^ { 40 } ergs s ^ { -1 } . No evidence is found for the presence of an active nucleus in the southern nucleus , contrary to previous speculation . Once the discrete sources are removed , the diffuse component has a soft spectrum which can be modelled by the superposition of 3 thermal plasma components with temperatures kT = 0.6 , 0.9 and 3.9 keV . Alternatively , the latter component can be described as a power-law with index \Gamma \sim 3 . Some evidence is found for a radial gradient of the amount of absorption and temperature of the diffuse component . We compare the X-ray emission with optical , H \alpha and NICMOS images of NGC3256 and find a good correlation between the inferred optical/near-IR and X-ray extinctions . Although Inverse Compton scattering could be important in explaining the hard X-rays seen in the compact sources associated with the nuclei , the observed diffuse emission is probably of thermal origin . The observed X-ray characteristics support a scenario in which the powerful X-ray emission is driven solely by the current episode of star formation .