  An upper bound to the supernova relic neutrino background from all past Type
II supernovae is obtained using observations of the Universal metal enrichment
history. We show that an unambiguous detection of these relic neutrinos by the
Super-Kamiokande detector is unlikely. We also analyze the event rate in the
Sudbury Neutrino Observatory (where coincident neutrons from anti-nu_e + D -->
n + n + e+ might enhance background rejection), and arrive at the same
conclusion. If the relic neutrino flux should be observed to exceed our upper
bound and if the observations of the metal enrichment history (for z<1) are not
in considerable error, then either the Type II supernova rate does not track
the metal enrichment history or some mechanism may be responsible for
transforming anti-nu_{mu,tau} --> anti-nu_e.
