We present the first calculation of Z + 4 jet production with heavy qu
ark flavor identification at the Tevatron <p(p)over bar> collider. The
Z + 4 jet channel is especially interesting as a normalizer for the W
+ 4 jet background to top quark signals, as a background to a possibl
e t --> cZ flavor-changing neutral-current (FCNC) decay signal, and as
a background to missing-p(tau) signals from gluino pairs. We also cal
culate the contributions to W + 4 jet production from all the differen
t heavy-flavor final states. The MADGRAPH program is used to generate
all leading order subprocess helicity amplitudes. We present Monte Car
lo results with separation and acceptance criteria suitable for the Te
vatron experimental analyses. The dependence of the cross sections on
experimental cuts and the theoretical ambiguities due to the scale dep
endence are discussed. The predicted (W + 4 jet)/(Z + 4 jet) ratio is
insensitive to most of these choices.