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 may use a two-handed weapon in one hand. You also gain a +2 to all checks using that hand only.
Drawback: You cannot wield a shield (or weapon) effectively with your other hand, you get a -1 to all rolls and checks (including AC) when using your other hand.
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).