We show that the information entropy {ital S}{sub {ital i}}, where {ital i} is the number of steps, is a good parameter to characterize chaoticity in branching processes. The quantity {ital S}{sub {ital i}}{minus}ln{l_angle}{ital n}{r_angle}{sub {ital i}}, where {l_angle}{ital n}{r_angle}{sub {ital i}} is the average number of particles produced at step {ital i}, approaches {minus}{infinity} in Abelian processes and a finite constant in non-Abelian ones. {copyright} {ital 1996 The American Physical Society.}