We consider the totally asymmetric simple exclusion process (TASEP) with a non-random initial condition that has a discontinuity (shock) in the particle density. If one inserts a "second class particle" in the system, it will follow the shock. For large time t, we show that the position of the second class particle fluctuates on the t^{1/3} scale and we determine its limiting law. Joint work with Patrik Ferrari and  Promit Ghosal.