Following the outburst of the unusual variable star V838 Monocerotis in 2002,
a spectacular light echo appeared. A light echo provides the possibility of
direct geometric distance determination, because it should contain a ring of
highly linearly polarized light at a linear radius of ct, where t is the time
since the outburst. We present imaging polarimetry of the V838 Mon light echo,
obtained in 2002 and 2005 with the Advanced Camera for Surveys onboard the
Hubble Space Telescope, which confirms the presence of the highly polarized
ring. Based on detailed modeling that takes into account the outburst light
curve, the paraboloidal echo geometry, and the physics of dust scattering and
polarization, we find a distance of 6.1+-0.6 kpc. The error is dominated by the
systematic uncertainty in the scattering angle of maximum linear polarization,
taken to be theta_{max}=90^o +- 5^o. The polarimetric distance agrees
remarkably well with a distance of 6.2+-1.5 kpc obtained from the entirely
independent method of main-sequence fitting to a sparse star cluster associated
with V838 Mon. At this distance, V838 Mon at maximum light had M_V\simeq-9.8,
making it temporarily one of the most luminous stars in the Local Group. Our
validation of the polarimetric method offers promise for measurement of
extragalactic distances using supernova light echoes.Comment: 43 pages, 17 figures, 3 tables; accepted for publication in the
Astronomical Journal. Version with high-quality figures available at
http://www.stsci.edu/~bond/v838monpolariz.pd