In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes as generated by Tchebyscheff maps, and show that the vacuum energy of these models is minimized for coupling constants that coincide with running standard model couplings at energy scales given by the known fermion and boson masses. Chaotic quantization thus allows to predict fundamental constants of nature from first principles. At the same time, it provides a natural framework to understand the dynamical origin of vacuum energy in our universe.