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We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions. We show that QNEC saturates for all solutions to vacuum AdS$_3$ Einstein gravity with Brown--Henneaux boundary conditions, including systems that are dual a CFT$_2$ far from thermal equilibrium. In the presence of bulk matter QNEC need not be saturated and can even be violated. We give both analytical and numerical examples exhibiting these features. Specifically, for CFT$_2$ with a local quench dual to AdS$_3$-Vadiya geometries we find a curious semi-saturation of QNEC. We close with three suggestive remarks: first, we advocate the notion of ``quantum equilibrium'' and equate it to QNEC saturation; second, we propose an operator interpretation for QNEC; third, we show that QNEC may provide new constraints on semi-classical model building of evaporating black holes and comment on relations between bulk and boundary energy conditions.
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