A new set of moments {ital G}{sub {ital q}} of the multiplicity distribution in a narrow rapidity window is suggested for analysis so that the chaotic fluctuations of the rapidity distribution can be described in the formalism of multifractals. Phenomenological evidence is given to show that there is a fractal structure in the data of multiparticle production at high energy. The fractal dimension and its generalizations can be determined to provide a description of the spectrum of scaling indices. The implication on the emergence of a new approach to the study of multiparticle production in the framework of multifractals in the theory of chaos is discussed.