We report the results of the Chandra ACIS subarcsecond resolution X-ray observation of the archetypal merger radio galaxy NGC 1316 (Fornax A). We confirm the presence of. ne substructures in the hot interstellar medium (ISM). Some of these are likely to result from interaction with the radio jets, while others may be related to a complex intermingling of different phases of the ISM. We detect a low-luminosity X-ray active galactic nucleus (AGN) with L-X = 5 x 10(39) ergs s(-1) (in 0.3-8 keV) and a Gamma = 1.7 power-law energy spectrum. We also detect 81 point sources within the 25th magnitude isophotal ellipse of NGC 1316 (LX in the range of 2 x 10(37) to 2 x 10(39) ergs s(-1)), with hard (kT similar to 5 keV) X-ray spectra, typical of X-ray binaries, and a spatial radial distribution consistent with that of the optical (i.e., stellar) surface brightness. We derive the X-ray luminosity function (XLF) of these sources, correcting for the incompleteness at the faint end caused by the presence of the diffuse emission from the hot ISM in the central regions of NGC 1316 and by the widening of the Chandra point-spread functions at increasing distance from the aim point. With these corrections, the XLF is well reproduced by a single-unbroken-power law with a slope of -1.3 down to our threshold luminosity of similar to3 x 10(37) ergs s(-1). The hot ISM has temperatures in the 0.5-0.6 keV range, its surface brightness distribution is more centrally concentrated than that of the point sources, and its temperature appears to decrease at larger radii. These properties suggest that the ISM may be subject to partial winds. Taking into account the spectral complexity of the ISM, and the presence of unresolved low luminosity X-ray sources ( which can be inferred from the spectra), we constrain the metal abundance of the hot ISM to be Z = 0.25-1.3 Z. (90% confidence).