  We report the results of a search for the anomalous production of a massive
particle decaying to four electrons via two Z^0 bosons in 1.1 fb^{-1} of p-pbar
collisions at sqrt(s)=1.96 TeV collected by the CDF II detector at Fermilab. We
employ optimized electron identification criteria to maximize acceptance and
efficiency. We estimate the backgrounds in the invariant mass range 500 - 1000
GeV/c^2 to be 0.028 +/- 0.009 (stat) +/- 0.011 (syst) events. We observe zero
events in this search region. Assuming a Randall-Sundrum graviton production
model, we set 95% CL limits on \sigma times BF(G -> Z^0 Z^0) < 4 - 6 pb,
depending on the graviton mass.
