We report magnetic, transport, neutron diffraction, and muon spin rotation data showing that Pb$_2$CoOsO$_6$, a newly synthesized metallic double-perovskite with a centrosymmetric space group at room temperature, exhibits a continuous second-order phase transition at 45 K to a magnetically ordered state with a non-centrosymmetric space group. The absence of inversion symmetry is very uncommon in metals, particularly metallic oxides. In contrast to the recently reported ferroelectric-like structural transition in LiOsO$_3$, the phase transition in Pb$_2$CoOsO$_6$ is driven by a long-range collinear antiferromagnetic order, with propagation vector $\textbf{k} = (\frac{1}{2},0,\frac{1}{2})$, which relieves the frustration associated with the symmetry of themagnetic exchanges. This magnetically-driven loss of inversion symmetry represents a new frontier in the search for novel metallic behavior.
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