The action potential (AP) is transmitted by the concerted action of voltage-gated ion channels. Thermodynamic fluctuations in channel proteins produce probabilistic gating behavior, causing channel noise. Miniaturizing signaling systems increases susceptibility to noise, and with many cortical, cerebellar, and peripheral axons <0.5 mum diameter [1, 2 and 3], channel noise could be significant [4 and 5]. Using biophysical theory and stochastic simulations, we investigated channel-noise limits in unmyelinated axons. Axons of diameter below 0.1 microm become inoperable because single, spontaneously opening Na channels generate spontaneous AP at rates that disrupt communication. This limiting diameter is relatively insensitive to variations in biophysical parameters (e.g., channel properties and density, membrane conductance and leak) and will apply to most spiking axons. We demonstrate that the essential molecular machinery can, in theory, fit into 0.06 microm diameter axons. However, a comprehensive survey of anatomical data shows a lower limit for AP-conducting axons of 0.08-0.1 microm diameter. Thus, molecular fluctuations constrain the wiring density of brains. Fluctuations have implications for epilepsy and neuropathic pain because changes in channel kinetics or axonal properties can change the rate at which channel noise generates spontaneous activity.