Not only aren't you ambidextrous, you're pretty uncoordinated with anything that takes more than 1 hand. But your gifted good arm has always been more than enough on its own, so that hasn't really held you back.
Requirements: 1st level background feat
Required for: None
Specifics: Character gains +5 bonus to Attack Bonus when unarmed or using one-handed, light, and throwing weapons, but suffers a -10 penalty to Attack Bonus when using two-handed weapons. Beyond that, you cant use dual-wielding.