We report limits on anomalous $ZZ\gamma$ and $Z\gamma\gamma$
couplings derived from an analysis of $Z$ + photon production based on
approximately 20 $pb^{-1}$ of $p\bar{p}$ collision data recorded by the
Collider Detector at Fermilab (CDF).  We observe good agreement with the
Standard Model expectation that all $Z\gamma$ couplings are zero.
Confidence level intervals for individual couplings and contours for pairs
of CP-conserving/violating $ZZ\gamma$ and $Z\gamma\gamma$ couplings are
presented.