We present 2 mu m polarization measurements of positions in the IRc2 and BN regions of the OrionMolecular Cloud (OMC-1) made with NICMOS Camera 2 (0.`2 resolution) on the Hubble Space Telescope. Our results are as follows: BN is similar to 29% polarized by dichroic absorption and appears to be the illuminating source for most of the nebulosity to its north and for up to similar to 5` to its south. Although the stars are probably all polarized by dichroic absorption, there are a number of compact but non-point-source objects that could be polarized by a combination of both dichroic absorption and local scattering of starlight. We identify several candidate YSOs, including an approximately edge-on bipolar YSO 8`7 east of BN, and a deeply embedded variable star. Additional strongly polarized sources are IRc2-B, IRc2-D, and IRc7, all of which are obviously self-luminous at mid-infrared wavelengths and may be YSOs. None of these is a reflection nebula illuminated by a star located near radio source I, as was previously suggested. Other IRc sources are clearly reflection nebulae: IRc3 appears to be illuminated by IRc2-B or a combination of the IRc2 sources, and IRc4 and IRc5 appear to be illuminated by an unseen star in the vicinity of radio source I, or by star n or IRc2-A. Trends in the magnetic field direction are inferred from the polarization of the 26 stars that are bright enough to be seen as NICMOS point sources. The most polarized star has a polarization position angle different from its neighbors by similar to 40 degrees, but in agreement with the grain alignment inferred from millimeter polarization measurements of the cold dust cloud in the southern part of OMC-1.