  We develop a new method to measure source proper motions in microlensing
events, which can partially overcome problems due to blending. It takes
advantage of the fact that the source position is known precisely from the
microlensing event itself. We apply this method to the event MOA-2011-BLG-262,
which has a short timescale t_E=3.8 day, a companion mass ratio q=0.0047 and a
very high or high lens-source relative proper motion mu_rel=20 mas/yr or 12
mas/yr (for two possible models). These three characteristics imply that the
lens could be a brown dwarf or a massive planet with a roughly Earth-mass
"moon". The probability of such an interpretation would be greatly increased if
it could be shown that the high lens-source relative proper motion was
primarily due to the lens rather than the source. Based on the long-term
monitoring data of the Galactic bulge from the Optical Gravitational Lensing
Experiment (OGLE), we measure the source proper motion that is small, mu_s =
(-2.3, -0.9) +- (2.8,2.6) mas/yr in a (North, East) Galactic coordinate frame.
These values are then important input into a Bayesian analysis of the event
presented in a companion paper by Bennett et al.
