We present the design for a recently approved instrument for the Keck Telescope. Called OSIRIS, it was inspired by the optical spectrograph TIGER of R. Bacon et al. and will utilize an infrared transmissive lenslet array to sample a rectangular field of view at close to the Keck diffraction limit. By packing the spectra very closely together (2 pixel rows per spectrum) and using the Rockwell Hawaii-2 detector (wavelengths between 1 and 2.5 microns), we will achieve a relatively large field of view (up to 6."4) while maintaining full broad-band spectral coverage at a resolution of 3900. Due to the extremely low backgrounds between night sky lines and at AO spatial samplings, the instrument will reach point source sensitivities several times fainter than any existing infrared spectrograph. We are also coupling a separate infrared AO camera dubbed SHARC to work as an acquisition camera and to monitor the point spread function's behavior during long spectroscopic exposures. Among the challenges of the instrument are: a fully cryogenic design, four spatial resolutions from 0."02 to 0."10, large aluminum optics for the spectrography, extremely repeatable spectral formats and a sophisticated data reduction pipeline.