Obfuscation is a technique for protecting hardware intellectual property (IP) blocks against reverse engineering, piracy, and malicious modifications. Current obfuscation efforts mainly focus on functional locking of a design to prevent black-box usage. They do not directly address hiding design intent through structural transformations, which is an important objective of obfuscation. We note that current obfuscation techniques incorporate only: (1) local, and (2) predictable changes in circuit topology. In this paper, we present SAIL, a structural attack on obfuscation using machine learning (ML) models that exposes a critical vulnerability of these methods. Through this attack, we demonstrate that the gate-level structure of an obfuscated design can be retrieved in most parts through a systematic set of steps. The proposed attack is applicable to all forms of logic obfuscation, and significantly more powerful than existing attacks, e.g., SAT-based attacks, since it does not require the availability of golden functional responses (e.g. an unlocked IC). Evaluation on benchmark circuits show that we can recover an average of around 84% (up to 95%) transformations introduced by obfuscation. We also show that this attack is scalable, flexible, and versatile.