  We demonstrate remote entanglement of trapped-ion qubits via a
quantum-optical fiber link with fidelity and rate approaching those of local
operations. Two ${}^{88}$Sr${}^{+}$ qubits are entangled via the polarization
degree of freedom of two photons which are coupled by high-numerical-aperture
lenses into single-mode optical fibers and interfere on a beamsplitter. A novel
geometry allows high-efficiency photon collection while maintaining unit
fidelity for ion-photon entanglement. We generate remote Bell pairs with
fidelity $F=0.940(5)$ at an average rate $182\,\mathrm{s}^{-1}$ (success
probability $2.18\times10^{-4}$).
