Prediction of the plastic strength of single crystals based on the collective dynamics of dislocations has been a challenge for computational materials science for a number of years. The difficulty lies in the inability of the existing dislocation dynamics (DD) codes to handle a sufficiently large number of dislocation lines, in order to be statistically representative and to reproduce experimentally observed microstructures. A new massively-parallel DD code is developed that is capable of modeling million-dislocation systems by employing thousands of processors. We discuss the general aspects of this code that make such large scale simulations possible, as well as a few initial simulation results.