  In this note, we establish the 2-D Quantum Inequalities - first proved by
Flanagan - for all CFTs with a causal holographic dual. Following the treatment
of Kelly \& Wall, we establish that the Boundary Causality Condition in an
asymptotic AdS spacetime implies the Quantum Inequalities on the boundary. Our
results extend easily to curved spacetime and are stable under deformations of
the CFT by relevant operators. We discuss higher dimensional generalizations
and possible connections to recent bounds on $a/c$ in 4-D CFTs.
