We report on our success in (i) fabricating stacks of small intrinsic Josephson junctions using the high temperature superconductor La_2-xSr_xCuO₄ (x ≈ 0.08), and carrying out a reliable measurement of their switching current distributions. The standard deviation of the switching current converged below ∼ 5 K, suggesting the occurrence of macroscopic quantum tunneling (MQT) below this temperature. It was also found that the distribution of switching current at MQT region is quite broader than that expected from the theoy of conventional single Josephson junction model.