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_Vsimeq-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.
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