It is crucial for scientific progress to be able to replicate scientific findings [1-4], because scientific claims should gain credence due to the reproducibility and replicability of their main supporting evidences. However, according to Nature’s survey of 1,576 researchers, more than 70% of the surveyed failed to reproduce another scientist’s experiments, and more than half agreed that there exists a significant “crisis of reproducibility” . Here we reveal a new classification of chaos: normal-chaos and ultra-chaos. Unlike a normal-chaos, statistics of an ultra-chaos are sensitive to small disturbances. Some illustrative examples of ultra-chaos are given here. It is found that statistical non-reproducibility is indeed an inherent property of an ultra-chaos that is at a higher-level of disorder than a normal-chaos. It is impossible in practice to replicate experimental/numerical results of an ultra-chaos even in statistical meanings, since random environmental noises always exist and are out of control. Thus, ultra-chaos is indeed an insurmountable objective obstacle of reproducibility and replicability. Similar to Goedel’s incompleteness theorem, such kind of “incompleteness of reproducibility” reveals a limitation of scientific researches. It opens a new door and possibility to study reproducibility crisis, statistical significance, computational fluid dynamics (CFD), chaos theory, turbulence theory, and so on.