We present a detailed spectral and spatial analysis of the galaxy cluster PKS 0745-191, using recent observations from the Chandra X-Ray Observatory. The data provide information on the temperature and metallicity of the intracluster medium, the distribution of emission throughout the cluster, morphology of the cluster core, and an independent mass estimate that can be compared to that from gravitational lensing. X-ray spectra extracted from the central 300 kpc (~2') are well described by a two-temperature plasma, and the mean cluster temperature is consistent with previously determined values. The distribution of both temperature and metallicity within the inner 360 kpc (23) of PKS 0745-191 is probed on scales of 8'' (~20 kpc), yielding a relatively constant abundance throughout the region and a strong temperature gradient (down to ~4-5 keV) within the central 215 kpc. β-model fits to the surface brightness profile of PKS 0745-191 indicate that a second β-model component is required to fit the inner ~10 kpc. Imaging analysis of the cluster core reveals an irregular morphology within the inner 50 kpc and confirms that the X-ray emission peak lies within 05 (the spatial resolution of Chandra) of both the optical and radio central cD positions. The cluster mass, based on both two-temperature and multiphase fits to the X-ray spectrum, is in close agreement with lensing mass estimates of PKS 0745-191.