Associative memories have been an active area of research over the last forty years (Willshaw et al., 1969; Kohonen, 1972; Hopfield, 1982) because they form a central component of many cognitive architectures (Pollack, 1988; Anderson & Lebiere, 1998). We focus specifically on associative memories that store associations between arbitrary pairs of neural states. When a noisy version of an input state vector is presented to the network, it must output a "clean" version of the associated state vector. We describe a method for building large-scale networks for online learning of associations using spiking neurons, which works by exploiting the techniques of the Neural Engineering Framework (Eliasmith & Anderson, 2003). This framework has previously been used by Stewart et al. (2011) to create memories that possess a number of desirable properties including high accuracy, a fast, feedforward recall process, and etcient scaling, requiring a number of neurons linear in the number of stored associations. These memories have played a central role in several recent neural cognitive models including Spaun, the world's largest functional brain model (Eliasmith et al., 2012), as well as a proposal for human-scale, biologically plausible knowledge representation (Crawford et al., 2013). However, these memories are constructed using an ne optimization method that is not biologically plausible. Here we demonstrate how a similar set of connection weights can be arrived at through a biologically plausible, online learning process featuring a novel synaptic learning rule inspired in part by the well-known Oja learning rule (Oja, 1989). We present the details of our method and report the results of simulations exploring the storage capacity of these networks. We show that our technique scales up to large numbers of associations, and that recall performance degrades gracefully as the theoretical capacity is exceeded. This work has been implemented in the Nengo simulation package (http://nengo.ca), which will allow straightforward implementations of spiking neural networks on neuromorphic hardware. The result of our work is a fast, adaptive, scalable associative memory composed of spiking neurons which we expect to be a valuable addition to large systems peforming online neural computation.