We report experimental evidence of macroscopic quantum tunneling in antiferromagnetic particles. The zero-field maximum in the dependence of the magnetic relaxation rate on the magnetic field in ferritin has been observed. This observation provides a new insight into the origin of the nonmonotonic field dependence of the blocking temperature reported recently by Gider et al. [J. Appl. Phys. 79, 5324 (1996)] and by Friedman et al. (unpublished). We argue that the effect comes from the resonant spin tunneling between matching spin levels and cannot be due to the interparticle interactions. Our findings are in agreement with the tunneling interpretation of earlier experiments in ferritin by Awschalom et al. [Phys. Rev. Lett. 68, 3092 (1992)].