Hash tables are a commonly used data structure used in many algorithms and applications. As applications and data scale, the efficient implementation of hash tables becomes increasingly important and challenging. In particular, memory capacity becomes increasingly important and entries can become asymmetrically chained across hash buckets. This chaining prevents two forms of parallelism: memory-level parallelism (allowing multiple prefetch requests to overlap) and memory-computation parallelism (allowing computation to overlap memory operations). We propose, herniated hash tables, a technique that exploits multi-level phase change memory (PCM) storage to expand storage at each hash bucket and increase parallelism without increasing physical space. The technique works by increasing the number of bits stored within the same resistance range of an individual PCM cell. We pack more data into the same bit by decreasing noise margins, and we pay for this higher density with higher latency reads and writes that resolve the more accurate resistance values. Furthermore, our organization, coupled with an addressing and prefetching scheme, increases memory parallelism of the herniated datastructure. We simulate our system with a variety of hash table applications and evaluate the density and performance benefits in comparison to a number of baseline systems. Compared with conventional chained hash tables on single-level PCM, herniated hash tables can achieve 4.8x density on a 4-level PCM while achieving up to 67% performance improvement.