We report the results of a search for the decay K(L)0 --> pi0pi0gamma
conducted by the E799 Collaboration at Fermilab. The amplitude for thi
s process vanishes to O(p4) in chiral perturbation theory, so a measur
ement of the decay would directly probe O(p) effects. This is the firs
t published search for this decay mode and we set a 90% confidence lev
el upper limit on the branching ratio of B(K(L)0 --> pi0pi0gamma) < 2.
3 X 10(-4).