Data from the NA31 experiment at the CERN SPS have been used for the f
irst search for the decay mode K-L --> 3 gamma. Seven events have been
found with an estimated background of 6.7 +/- 1.5 events. The corresp
onding upper limit for the branching ratio is Gamma(K-L +/- 3 gamma)/G
amma(K-L --> all) = 2.4 x 10(-7) at the 90% confidence level, assuming
a phase-space decay distribution.