  We present the results of the first search for a new particle X produced in
$p\bar{p}$ collisions at \sqrt{s}=1.96 TeV and subsequently decaying to
Z\gamma. The search uses 0.3 fb$^{-1}$ of data collected with the D{\O}detector
at the Fermilab Tevatron Collider. We set limits on the production cross
section times the branching fraction $\sigma(p \bar{p} \to X) \times B(X\to
Z\gamma)$ that range from 0.4 -- 3.5 pb at the 95% C.L. for $X$ with invariant
masses between 100 and 1000 GeV/$c^2$ over a wide range of $X$ decay widths.
