  Controlling quantum entanglement between parts of a many-body system is the
key to unlocking the power of quantum information processing for applications
such as quantum computation, high-precision sensing, and simulation of
many-body physics. Spin degrees of freedom of ultracold neutral atoms in their
ground electronic state provide a natural platform given their long coherence
times and our ability to control them with magneto-optical fields, but creating
strong coherent coupling between spins has been challenging. We demonstrate a
Rydberg-dressed ground-state blockade that provides a strong tunable
interaction energy ($\sim$1 MHz in units of Planck's constant) between spins of
individually trapped cesium atoms. With this interaction we directly produce
Bell-state entanglement between two atoms with a fidelity $\geq$ 81(2)%,
excluding atom loss events, and $\geq$ 60(3)% when loss is included.
