The production rate and kinematics of photons produced in association with Z bosons are studied using 2  fb−1 of pp collision data collected at the Collider Detector at Fermilab. The cross section for pp→ℓ+ℓ−γ+X (where the leptons ℓ are either muons or electrons with dilepton mass Mℓℓ>40  GeV/c2, and where the photon has transverse energy EγT>7  GeV and is well separated from the leptons) is 4.6±0.2(stat)±0.3(syst)±0.3(lum)  pb, which is consistent with standard model expectations. We use the photon ET distribution from Zγ events where the Z has decayed to μ+μ−, e+e−, or νν to set limits on anomalous (non standard model) trilinear couplings between photons and Z bosons.