  We derive a simple empirical photometric redshift estimator using a training
set of galaxies with multiband photometry and measured redshifts in the Hubble
Deep Field (HDF). This estimator is model-independent; it does not use spectral
templates. The dispersion between the estimated redshifts and the
spectroscopically measured ones is small; the dispersions range from
$\sigma_z\simeq 0.03$ to 0.1 for $z\la 2$ galaxies, and from $\sigma_z\simeq
0.14$ to 0.25 for $z\ga 2$ galaxies. The predictions provided by our empirical
redshift estimator agree well with recently measured galaxy redshifts. We
illustrate how our empirical redshift estimator can be modified to include flat
spectrum galaxies with $1.4\la z \la 2$.
