Atomic two-photon J = 0 <-> J' = 1 transitions are forbidden for photons of
the same energy. This selection rule is related to the fact that photons o
bey Bose-Einstein statistics. We hare searched for small violations of this
selection rule by studying transitions in atomic Ba. We set a limit on the
probability nu that photons are in exchange-antisymmetric states: nu = 1.2
< x 10(-7).