This is a project to design and build a facility-class infrared cross-dispersed spectrograph instrument for the Infrared Telescope Facility which will provide a resolving power of up to 80,000 at 1.1 - 2.0 microns and 67,000 at 3 - 5 microns. The spectrograph is designed around a silicon immersion grating which not only reduces the size of the instrument but also permits high spectral resolution without requiring an extremely narrow slit. The use of the silicon immersion grating is important as this will be the first application on a 1-5 meter facility instrument and will therefore be an important demonstration of this technology for future instrumentation on the next generation of large telescopes. Observing time at the Infrared Telescope Facility is available to the general astronomical community so that this spectrograph will have a significant broader impact. The project will also train astronomy graduate students.