  We propose a two-qubit gate for neutral atoms in which one of the logical
state components adiabatically follows a two-atom dark state formed by the
laser coupling to a Rydberg state and a strong, resonant dipole-dipole exchange
interaction between two Rydberg excited atoms. Our gate exhibits optimal
scaling of the intrinsic error probability $E \propto (B\tau)^{-1}$ with the
interatomic interaction strength $B$ and the Rydberg state lifetime $\tau$.
Moreover, the gate is resilient to variations in the interaction strength, and
even for finite probability of double Rydberg excitation, the gate does not
excite atomic motion and experiences no decoherence due to
internal-translational entanglement.
