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The rotational spectra of the complexes Ar-CuF, Ar-CuCl and Ar-CuBr have been measured between 5-22 GHz using a cavity pulsed jet Fourier transform microwave spectrometer. They were prepared by ablating Cu metal with a Nd: YAG laser (532 nm) and allowing the vapour to react with a suitable precursor contained as in the Ar backing gas of the jet. The complexes are linear and rather rigid, with the Ar-Cu stretching frequency estimated as $\sim 200cm-1$. Ground state effective $(ro$) and, where possible, substitution ($rs$,) and double substitution ($rd$) geometries have been obtained. The Ar-Cu bonds are short (2.22-2.30{\AA}). Large changes in the Cu nuclear quadrupole coupling constants indicate extensive charge rearrangement on complex formation. Ab initio calculations at the MP2 level of theory predict an Ar-Cu bond energy in Ar-CuF of $\sim 47kJmol-1$, along with a transfer of $\sim 0.1$ electron from Ar to Cu. The whole picture is consistent with weak Ar-Cu covalent bonding.