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We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by . Using two different gate protocols we measure CNOT fidelities of and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity . After correcting for atom loss we obtain an a posteriori entanglement fidelity of .