We report on H-band spectra of chemically peculiar Mercury-Manganese (HgMn) stars obtained via the SDSS/APOGEE survey. As opposed to other varieties of chemically peculiar stars such as classical Ap/Bp stars, HgMn stars lack strong magnetic fields and are defined by extreme overabundances of Mn, Hg, and other heavy elements. A satisfactory explanation for the abundance patterns remains to be determined, but low rotational velocity is a requirement and involvement in binary/multiple systems may be as well. The APOGEE HgMn sample currently consists of 269 stars that were identified among the telluric standard stars as those whose metallic absorption content is limited to or dominated by the H-band Mn ii lines. Due to the fainter magnitudes probed by the APOGEE survey as compared to past studies, only 9/269 stars in the sample were previously known as HgMn types. The 260 newly identified HgMn stars represents a more than doubling of the known sample. At least 32 per cent of the APOGEE sample are found to be binary or multiple systems, and from multi-epoch spectroscopy, we were able to determine orbital solutions for at least one component in 32 binaries. Many of the multilined systems include chemically peculiar companions, with noteworthy examples being the HgMn+Ap/Bp binary HD 5429, the HgMn+HgMn binary HD 298641, and the HgMn+Bp Mn + Am triple system HD 231263. As a further peculiarity, roughly half of the sample produces narrow emission in the C i 16895 Å line, with widths and radial velocities that match those of the Mn ii lines.