Effects of the slowly varying control parameters on bifurcations of the equilibria and limit cycles have been previously studied in detail. In this paper, the concept of dynamic bifurcations is extended to chaotic phenomena. We consider this problem for a Lorenz-type map. As the control parameter passes through a critical value, the dynamic boundary crisis of a chaotic attractor takes place. We discover and analyze the effects of delayed exit from the chaotic region and non-exponential decay of the number of surviving trajectory points. The property of the delay increase with increasing rate of the control parameter change has also been demonstrated and explained.