A Hopfield Neural Network is a content addressable memory with elements consisting of the correlations between elements of memory vectors. Recall of a complete memory vector is possible via the introduction of a "corrupted" vector, which is a memory vector with some components altered. It may also be possible to correctly recall memories with the use of a partial vector. It may be possible to create such an information storage and retrieval system using DNA as a working substance. Herein I present some computational results for properties of Hopfield Neural Networks, as well as a theoretical framework for the operation of such a system, including possible limitations in the working substance.