A very fast 3D prestack Kirchhoff depth migration algorithm is developed. The computational cost is significantly reduced by six features. First, ray parameter information for the incident wave directions at the receiver locations is measured from input 3D seismic data in common source gathers and is used to reduce the amount of ray tracing required. Second, ray angles are binned and the ray corresponding to an angle bin is computed only once, regardless of how many times it occurs on a seismic trace. Third, the ray parameter file structure is optimized to eliminate redundancy associated with the overlap of seismic traces sharing the same receiver location. Fourth, fast two-point ray tracing is used to find the stationary reflection point on the receiver ray path that satisfies the time imaging condition. Fifth, the migration impulse response operator is reduced to the first Fresnel zone around the estimated stationary reflection point, which is much smaller than the large isochronic surface within the migration aperture in traditional Kirchhoff migration. Sixth, an amplitude threshold value is applied to decimate the input seismic data volume. The first four factors obviate the traditional traveltime table calculation before migration. Traveltime computation is embedded into the migration in the new algorithm. 3D synthetic prestack data test examples show that the new algorithm is two to three orders of magnitude faster than the traditional prestack Kirchhoff depth migration. The parsimonious images are cleaner than those obtained by traditional Kirchhoff migration, but are slightly less coherent.