The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy, Al0.3CoCrCuFeNi, were analyzed for the nanoindentation performed at two temperatures. Critical behavior of serrations at room temperature and chaotic flows at 200 degrees C were detected. These results are attributed to the interaction among a large number of slip hands. For the nanoindentation at room temperature, recurrent partial events between slip hands introduce a hierarchy of length scales, leading to a critical state. For the nanoindentation at 200 degrees C, there is no spatial interference between two slip hands, which is corresponding to the evolution of separated trajectory of chaotic behavior.