An upper limit for BR(Z(0) --> 3g) is obtained from a correlation method, which distinguishes statistically between quark and gluon jets by using the difference in their charged particle multiplicity distributions. From the sample of threefold symmetric three-jet events collected by the DELPHI experiment at LEP during 1991-1994, the 95% confidence level upper limit is deduced to be: BR(Z(0) --> 3g) less than or equal to 1.6 x 10(-2) for the JADE and BR(Z(0) --> 3g) less than or equal to 1.5 x 10(-2) for the DURHAM jet-finder.
