We report the development of the first high resolution cross-dispersed silicon immersion grating spectrometer. This instrument is called the Florida IR Silicon immersion grating specTrometer (FIRST). FIRST can produce R = 50,000 under a 0.6 arcsec seeing and simultaneously cover 1.3-1.8 μm with a 1k×1k HgCdTe array at the Apache Point Observatory 3.5 meter telescope. FIRST has a 50 mm diameter collimated beam and the overall instrument is within a volume of 0.8×0.5×0.5 m 3. The high dispersion, large wavelength coverage and small instrument volume become possible due to the use of a silicon immersion grating (54.7 deg blaze angle and 50 mm diameter entrance pupil) with extremely high dispersion power (3.4 times dispersion power of a conventional echelle) and coarse grooves (16.1 1/mm, coarser than the commercially available echelles). The silicon immersion grating used in a lab bench mounted Czeney-Turner spectrograph with an only 25 mm diameter collimated beam and a 100 um core fiber has produced R = 55,000 cross-dispersed solar spectra. This instrument is designed to precisely measure radial velocities of low mass stars, M dwarfs for detecting 5-10 Earth mass planets. The estimated Doppler precision is ∼ 3 m/s for a J = 9 M5V dwarf in 15 min at the APO 3.5m telescope.