We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312] when a proximal electronic spin associated with a nitrogenvacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment.Nuclear spins are of fundamental importance for storage and processing of quantum information. Their excellent coherence properties make them a superior qubit candidate even in room temperature solids. Unfortunately, their weak coupling to the environment also makes it difficult to isolate and manipulate individual nuclei. Recently, coherent preparation, manipulation and readout of individual 13 C nuclear spins in the diamond lattice were demonstrated [1,2]. These experiments make use of optical polarization and manipulation of the electronic spin associated with a nitrogen-vacancy (NV) color center in the diamond lattice [3,4,5,6]. This enables reliable control of the nuclear spin qubit via hyperfine interactions with the electronic spin.In order to be useful for applications in scalable quantum information processing [3], such as quantum communication [7] and quantum computation [8], the quantum coherence of the nuclear spins must be maintained even when the electronic state is undergoing fast transitions associated with optical measurement and with entanglement generation between electronic spins. In this Letter, we investigate coherence properties of such an optically illuminated nuclear spin-electron spin system. We show that these properties are well-described by a spin-fluctuator model [9,10,11,12], involving a single nuclear spin (system) coupled by the hyperfine interaction to an electron [13] (fluctuator) that undergoes rapid optical transitions and mediates the coupling between the nuclear spin and the environment. We generalize the spin-fluctuator model to a vector description, necessary for single NV centers in diamond [1], and make direct comparisons with experiments. Most importantly we demonstrate that the decoherence of the nuclear spin due to the rapidly fluctuating electron is greatly suppressed via a mechanism analogous to motional narrowing in nuclear magnetic resonance (NMR) [14,15], allowing the nuclear spin coherence to be preserved even after hundreds of optical excitation cycles. We further show that by proper tuning of experimental parameters it may be possible to completely decouple the nuclear spin system from the electronic environment. The spinfluctuator model discussed here ...