Unidextrous (3.5e Trait)
From D&D Wiki
You have favored one hand for your entire life, all that work has made it better.
Benefit: You also gain a +1 to all attack rolls while wielding a single weapon one-handed in your primary hand if your other hand is empty.
Drawback: You cannot wield a shield (or weapon) effectively with your other hand, you get a -2 to attack rolls and AC when both hands are holding weapons and/or shields.
Roleplaying Ideas: You character will only use the one hand, while walking his other arm will just hang (while his favored hand will move with his momentum).