JWST spectroscopy has revolutionized our understanding of galaxies in the early universe. Covering wavelengths up to \(5.3\,{\rm \mu m}\), NIRSpec can detect rest-frame optical emission lines H\(\alpha\) out to \(z = 7\) and O III to \(z = 9.5\). Observing these lines in more distant galaxies requires longer wavelength spectroscopy with MIRI. Here we present MIRI MRS IFU observations of the lensed galaxy merger MACS0647\(-\)JD at \(z = 10.165\). With exposure times of 4.2 hours in each of two bands, we detect H\(\alpha\) at \(9\sigma\), O III\(\,\lambda5008\) at \(11\sigma\), and O III\(\,\lambda4960\) at \(3\sigma\). Combined with previously reported NIRSpec spectroscopy that yields seven emission lines including the auroral line O III\(\,\lambda4363\), we present the first direct metallicity measurement of a \(z > 10\) galaxy: \(12+{\rm log(O/H)}= 7.79\pm0.09\), or \(0.13^{+0.02}_{-0.03}\,Z_{\odot}\). This is similar to galaxies at \(z \sim 4 - 9\) with direct metallicity measurements, though higher than expected given the high specific star formation rate \({\rm log(sSFR / yr^{-1})} = -7.4 \pm 0.3\). We further constrain the ionization parameter \({\rm log}(U)\) = \(-1.9 \pm 0.1\), ionizing photon production efficiency \({\rm log}(\xi_{\rm ion})\) = \(25.3\pm0.1\), and star formation rate \(5.0\pm0.6\,M_{\odot}/{\rm yr}\) within the past \(10\,{\rm Myr}\). These observations demonstrate the combined power of JWST NIRSpec and MIRI for studying galaxies in the first \(500\) million years.