electrochemistry - Why is chloride oxidised instead of water in copper chloride electrolysis?

For the Electrolysis of Copper Chloride:

Cathode: $\ce{Cu^{2+} + 2e- <=> Cu}$
Anode: $\ce{2Cl <=> Cl2 + 2e- }$

I am confused about the reaction taking place at the anode. Wouldn't $\ce{H2O}$ rather undergo oxidation since it has an increased reducing ability? eg. It is above $\ce{2Cl-}$ on the Table of Standard Reduction Potentials.

Am I missing something? Or do all halogens discharge more readily than water?