  We present a new approach to measuring the thickness of a partially face-on
stellar disk, using dust geometry. In a moderately-inclined disk galaxy, the
fraction of reddened stars is expected to be 50% everywhere, assuming that dust
lies in a thin midplane. In a thickened disk, however, a wide range of radii
project onto the line of sight. Assuming stellar density declines with radius,
this geometrical projection leads to differences in the numbers of stars on the
near and far sides of the thin dust layer. The fraction of reddened stars will
thus differ from the 50% prediction, with a deviation that becomes larger for
puffier disks. We map the fraction of reddened red giant branch (RGB) stars
across M31, which shows prominent dust lanes on only one side of the major
axis. The fraction of reddened stars varies systematically from 20% to 80%,
which requires that these stars have an exponential scale height h_z that is
0.14+/-0.015 times the exponential scale length (h_r~5.5kpc). M31's RGB stars
must therefore have h_z=770+/-80pc, which is far thicker than the Milky Way's
thin disk, but comparable to its thick disk. The lack of a significant thin
disk in M31 is unexpected, but consistent with its interaction history and high
disk velocity dispersion. We suggest that asymmetric reddening be used as a
generic criteria for identifying ``thick disk'' dominated systems, and discuss
prospects for future 3-dimensional tomographic mapping of the gas and stars in
M31.
