We present linear polarization observations of the bipolar outflow source OH 0739-14 from 1.2 to 3.6 μm. The high levels of polarization (∼47% in the bipolar lobes) and the angles of the vectors in the outflow lobes imply that the 1.2-3.6 μm polarization is due to single scattering by dust grains of light from the central source or from its immediate vicinity. Our polarization measurements, combined with phase-lag measurements of variability in the nebula by Kastner et al. [ApJ, 398, 552 (1992)], tightly constrain the inclination angle i between the bipolar axis and the plane of the sky to be 35°≤i≤37°. We observe the percentage polarization of the bipolar lobes to be constant with wavelength from 1.2 to 3.6 μm, which rules out any significant contribution by unpolarized emission, such as tiny grain emission, to the 3.6 μm emission. We propose to explain the K-L′ color of the nebula as due to illumination by both the central star and by thermal emission from dust in a surrounding circumstellar shell with a dust temperature of 600-1000 K. Using this model, we find a relatively high minimum scattering optical depth at 3.75 μm of τω>0.1. This is difficult to reconcile with Rayleigh scattering, which would then imply optically thick scattering at wavelengths of 1.2 and 1.65 μm, in contrast to the observations. We also find that the albedo of the grains at 3.75 μm and probably at 2.2 μm is higher than predicted for normal interstellar grains.