  We examine the phase evolution of a Bose-Einstein condensate of photons
generated in a dye microcavity by temporal interference with a phase reference.
The photo-excitable dye molecules constitute a reservoir of variable size for
the condensate particles, allowing for grand canonical statistics with photon
bunching, as in a lamp-type source. We directly observe phase jumps of the
condensate associated with the large statistical number fluctuations and find a
separation of correlation timescales. For large systems, our data reveals phase
coherence and a spontaneously broken symmetry, despite the statistical
fluctuations.
