[en] A scheme is presented for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a 'magic' wavelength that does not perturb the clock frequency - to maintain clock accuracy - while an open-shell J=1/2 'head' atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent 'Archimedes' screw' transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, J=0, clock states of bosonic isotopes of divalent atoms. The on-site interactions between the clock atoms and the head atom are used to engineer entanglement and for clock readout.