We have developed and implemented a computer algorithm to perform Kirchhoff 3-D prestack time migration of seismic reflection data on the massively parallel Connection Machine architecture. Our algorithm runs at 427 Mflop/s on an 8k processor CM with 64 Mb core memory, and is scalable to over 3.4 Gflop/s on a full 64k processor Connection Machine. Our migration code allows heterogeneous time migration velocities and arbitrary trace binning, both of which are advantageous in 3-D processing. The present geometry of our algorithm is well-suited to situations in which the image volume dimensions are similar to or smaller than the acquisition aperture. If the image volume is much larger than the survey aperture, the code may require modification to incorporate migration aperture more efficiently. Finally, at these rapid computational speeds, it becomes feasible to contemplate real applications in 3-D prestack migration velocity analysis, migration impedance inversion, and seismic reservoir characterization.