The effectiveness of CAPTCHA challenges largely depends on being simultaneously easier to solve for humans and harder to solve for bots. In this work we argue that it is possible to enhance the effectiveness of audio CAPTCHA challenges by adapting the challenge to the users characteristics. We propose a method for achieving this adaptation while protecting users privacy. Moreover, our approach allows us to address discrimination issues that naturally arise in contemporary audio CAPTCHA challenges. Utilizing modern cryptographic techniques we design a privacy-preserving system, called PrivCAPTCHA, which offers customized CAPTCHA challenges.