Under Options is an ability that allows you to hide your opponent's Chat in Player vs Player combat. If you have this option enabled, during a PvP duel:
Anything you type cannot be seen by your opponents, but can be seen by your teammates and spectators.
Anything your opponents type you can’t see, but can be seen by their teammates and spectators.
All Menu Chat can be seen by everyone.
You can change this setting at any time, including during a PvP duel, but it will not take affect until the next turn.