Résumé : An upper limit for BR(Z0 -»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(Zn -> 3g) < 1.6 x 10~2 for the JADE and BR(Z0 -> 3g) < 1.5 x 10~2 for the DURHAM jet-finder.