It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by fluctuations of the synaptic inputs around their mean. It remains unclear whether neural networks in the balanced state can perform tasks that are highly sensitive to noise, such as storage of continuous parameters in working memory, while also accounting for the irregular behavior of single neurons. Here we show that continuous parameter working memory can be maintained in the balanced state, in a neural circuit with a simple network architecture. We show analytically that in the limit of an infinite network, the dynamics generated by this architecture are characterized by a continuous set of steady balanced states, allowing for the indefinite storage of a continuous parameter. In finite networks, we show that the chaotic noise drives diffusive motion along the approximate attractor, which gradually degrades the stored memory. We analyze the dynamics and show that the slow diffusive motion induces slowly decaying temporal cross correlations in the activity, which differ substantially from those previously described in the balanced state. We calculate the diffusivity, and show that it is inversely proportional to the system size. For large enough (but realistic) neural population sizes, and with suitable tuning of the network connections, the proposed balanced network can sustain continuous parameter values in memory over time scales larger by several orders of magnitude than the single neuron time scale.