We describe the design and performance of the Near Infrared Telescope Experiment (NITE), a rocket-borne instrument designed to search for infrared emission from baryonic dark matter in the halos of nearby edge-on spiral galaxies. A 256 x 256 InSb array at the focus of a 16.5 cm liquid-helium-cooled telescope achieves near-background-limited sensitivity in a 3.5 - 5.5 mu m waveband where the local foreground from zodiacal emission is at a minimum. This experiment represents the first scientific application of a low-background infrared InSb array, a precursor to the InSb arrays intended for SIRTF, in a spaceborne observation. We describe the night performance of the instrument and preliminary scientific results from an observation of NGC 4565.