Employers sometimes use personality tests in hiring or specifically look for candidates with certain personality traits such as being social, outgoing, active, and extraverted. Therefore, they hire based on personality, specifically extraversion in part at least. The question arises whether this practice is morally permissible. We argue that, in a range of cases, it is not. The common belief is that, generally, it is not permissible to hire based on sex or race, and the wrongness of such hiring practices is based on two widely accepted principles: the Relevance Principle and the Fairness Principle. The Relevance Principle states that hiring should be based on what is relevant to job performance, while the Fairness Principle states that hiring should be based on features that individuals can control. Since hiring based on sex or race violates these principles, it is wrong. However, we argue that, in a range of cases, hiring based on extraversion also violates these principles, and assuming the validity of the Relevance and the Fairness Principles, it follows that personality discrimination is morally wrong in those cases.