Associative memories are capable of memorizing particular patterns and recalling them from their partial information. Different from simple associative memory models based on Hopfield neural networks with sigmoid neurons, a particular model based on the chaotic neural network was also proposed for dynamic associative memory, which can generate various patterns from given information. However, the chaotic network model is so complicated that its behavior has not been analyzed well and can't be controlled easily. To the contrary, this paper shows that a discrete-time simple associative memory model with Euler's difference scheme has possibility to generate chaos. It follows that even such a simple model can be used for dynamic associative memory. Numerical examples also confirm the emergence of chaotic trajectories of the model and demonstrate their use for dynamic associative memory.