Cache timing attacks allow attackers to infer the properties of a secret execution by observing cache hits and misses. But how much information can actually leak through such attacks? For a given program, a cache model, and an input, our CHALICE framework leverages symbolic execution to compute the amount of information that can possibly leak through cache attacks. At the core of CHALICE is a novel approach to quantify information leak that can highlight critical cache side-channel leaks on arbitrary binary code. In our evaluation on real-world programs from OpenSSL and Linux GDK libraries, CHALICE effectively quantifies information leaks: For an AES-128 implementation on Linux, for instance, CHALICE finds that a cache attack can leak as much as 127 out of 128 bits of the encryption key.