  KH 15D is a strongly variable T Tauri star in the young star cluster NGC 2264
that shows a decrease in flux of 3.5 magnitudes lasting for 18 days and
repeating every 48 days. The eclipsing material is likely due to orbiting dust
or rocky bodies in a partial ring or warped disk that periodically occults the
star. We measured the polarized spectrum in and out of eclipse at the Keck and
Palomar observatories. Outside of the eclipse, the star exhibited low
polarization consistent with zero. During eclipse, the polarization increased
dramatically to ~2% across the optical spectrum, while the spectrum had the
same continuum shape as outside of eclipse and exhibited emission lines of much
larger equivalent width, as previously seen. From the data, we conclude that
(a) the scattering region is uneclipsed; (b) the scattering is nearly
achromatic; (c) the star is likely completely eclipsed so that the flux during
eclipse is entirely due to scattered light, a conclusion also argued for by the
shape of the ingress and egress. We argue that the scattering is not due to
electrons, but may be due to large dust grains of size ~10 micron, similar to
the interplanetary grains which scatter the zodiacal light. We construct a
warped-disk model with an extended dusty atmosphere which reproduces the main
features of the lightcurve, namely (a) a gradual decrease before ingress due to
extinction in the atmosphere (similar for egress); (b) a sharper decrease
within ingress due to the optically-thick base of the atmosphere; (c) a
polarized flux during eclipse which is 0.1% of the total flux outside of
eclipse, which requires no fine-tuning of the model. (abridged)
