  We report on time resolved measurements of the first order spatial coherence
in an exciton polariton Bose-Einstein condensate. Long range spatial coherence
is found to set in right at the onset of stimulated scattering, on a picosecond
time scale. The coherence reaches its maximum value after the population and
decays slower, staying up to a few hundreds of picoseconds. This behavior can
be qualitatively reproduced, using a stochastic classical field model
describing interaction between the polariton condensate and the exciton
reservoir within a disordered potential.
