The discrete model, approximating with exponential accuracy the set of interacting closed vortex lines in an ideal fluid, is proposed and investigated by means of the computer. The vortex lines move in their own velocity field according to the Biot-Savart law. This is a generalized Hamiltonian system possessing in addition an infinite number of conservation laws. Nevertheless, the motion becomes stochastic for certain initial conditions, and may be interpreted as marking the onset of turbulence.