We introduce the concept of an analog neural network represented by chemical operations performed on strands of DNA. This new type of DNA computing has the advantage that it should be fault tolerant and thus more immune to DNA hybridization errors than a Boolean DNA computer. We describe a particular set of DNA operations to effect the interconversion of electrical and DNA data and to represent the Hopfield associative memory and the feed-forward neural network of Rumelhart et al. We speculate that networks containing as many as 10(9) neurons might be feasible.