We present new results of numerical simulations for driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics of vortices display dissipative chaos. Intermittency routes to chaos have been clearly identified below the differential resistance peak. The peak region is characterized by positive Lyapunov exponents characteristic of chaos, and low frequency broad-band noise. Furthermore we find a low fractal dimension of the strange attractor, which suggests that only a few dynamical variables are sufficient to model the complex plastic dynamics of vortices.