The first principle calculations of quantum chaos in the framework of representation constructed by authors for multi-channel quantum scattering was made. Based on intrinsic properties of scattering system the numerical task was divided into independent subtasks and the parallel algorithm for numerical computations was developed and tested on massive-parallel systems Parsytec CC/16 and SPP-1600. This algorithm made it possible to carry out converging computations for three-body problem for any energy. It was shown, that even in the simple case of three-body problem the principle of quantum determin- ism breaks down in general and one has a micro-irreversible quantum mechanics. The ab initio calculations of the quantum chaos (wave chaos) were carried out on the example of an elementary chemical reaction (Formula Presented.).