  We demonstrate precise control of the coupling of each of two trapped ions to
the mode of an optical resonator. When both ions are coupled with near-maximum
strength, we generate ion--ion entanglement heralded by the detection of two
orthogonally polarized cavity photons. The entanglement fidelity with respect
to the Bell state $\Psi^+$ reaches $F \geq (91.9\pm2.5)%$. This result
represents an important step toward distributed quantum computing with cavities
linking remote atom-based registers.
