We report on a Chandra observation of the massive, medium redshift (z = 0.1386) cooling flow cluster A1068. We detect a clear temperature gradient in the X-ray-emitting gas from kT similar to 5 keV in the outer part of the cluster down to roughly 2 keV in the core and a striking increase in the metallicity of the gas toward the cluster center. The total spectrum from the cluster can be fitted by a cooling flow model with a total mass deposition rate of similar to150 M-circle dot yr(-1). Within the core (r < 30 kpc), the mass deposition rate of similar to 40 M-circle dot yr(-1) is comparable to estimates for the star formation rate from optical data. We find an apparent correlation between the cD galaxy's optical isophotes and enhanced metallicity isocontours in the central similar to 100 kpc of the cluster. We show that the approximate doubling of the metallicity associated with the cD galaxy can be plausibly explained by supernova explosions associated with the cD galaxy's ambient stellar population and the recent starburst. Finally, we calculate the amount of heating due to thermal conduction and show that this process is unlikely to offset cooling in A1068.