CAPTCHAs are essentially challenge-response tests that are used to distinguish whether a user is a human or a computer. To date, numerous CAPTCHA schemes have been proposed and deployed on various websites to secure online services from abuse by automated programs. However, many of these CAPTCHAs have been found to suffer from design flaws that can be exploited to break the CAPTCHA. Hence, the development of a good CAPTCHA scheme that is both secure and human usable is an important research problem. This paper addresses this problem by presenting AniCAP, a new animated 3D CAPTCHA scheme that is designed to capitalize on the difference in ability between humans and computers at the task of perceiving depth through motion. In this paper, we present the design of AniCAP, along with a formal definition of its underlying Artificial Intelligence (AI) problem family. In addition, we analyze the security issues and considerations concerning AniCAP.