We describe a successful effort to produce a laser comb around 1.55 $mu$m in the astronomical H band using a method based on a line-referenced, electro-optical-modulation frequency comb. We discuss the experimental setup, laboratory results, and proof of concept demonstrations at the NASA Infrared Telescope Facility (IRTF) and the Keck-II telescope. The laser comb has a demonstrated stability of $<$ 200 kHz, corresponding to a Doppler precision of ~0.3 m/s. This technology, when coupled with a high spectral resolution spectrograph, offers the promise of $<$1 m/s radial velocity precision suitable for the detection of Earth-sized planets in the habitable zones of cool M-type stars.