We discuss the design of a Transition Edge Sensor (TES) based Cryogenic Hard X-ray Imaging Spectrometer (CHXIS) which could be used underneath the International X-ray Observatory (IXO) X-ray Microcalorimeter Spectrometer (XMS). The XMS is required to observe astrophysical sources in the soft X-ray 0.3-10 keV bandpass. The IXO hard X-ray mirror module, however, will incorporate multilayer coatings to enhance response up to 40 keV, and inclusion of the CHXIS would extend the instrument bandpass accordingly. X-rays not absorbed in the XMS would be incident on the CHXIS; a 1 mm thick germanium CHXIS would have quantum efficiencies of 96%, 39% and 25% at 40, 80 and 100 keV respectively, with negligible Compton scattering. We are targeting an energy resolution of 500 eV at 40 keV which would be limited by Fano statistics and charge carrier recombination in the Ge bulk. The CHXIS is one possible proposal for extending the energy range of the XMS beyond the 0.2-10 keV reference design. The use of TESs makes the CHXIS compatible with existing XMS SQUID readout electronics. In this design, the absorber is divided into a small number of macropixels to reduce the number of XMS readout channels dedicated to the CHXIS. Each macropixel would have 4 phonon channels to simultaneously determine energy and position of the X-ray interaction. The position resolution is expected to exceed IXO's 30 arcsec imaging resolution by an order of magnitude. By differentiating X-rays from minimum-ionizing cosmic rays, this type of detector could also be used as an XMS anti-coincidence detector.