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Using solid state multiple pulse techniques the magnetic shielding tensors σ of the 19F nuclei in a single crystal of KZnF3 have been measured. The F--site symmetry in KZnF3, D4h , allows axial anisotropy of σ and determines fully the principal shielding directions. Using CaF2 as the reference compound, the average shielding is + 85 ppm and the shielding anisotropy is + 18.4 ppm. These results are discussed in terms of shielding contributions from (a) the closed shell electrons of the F--ion whose shielding is considered, (b) the closed shell electrons of the neighbouring metal and fluorine ions and (c) weak admixture of covalency to the predominantly ionic Zn++-F- bonding.