Single-file diffusion behavior is expected for atoms and molecules in one-dimensional gas phases of nanochannels with transverse dimensions that do not allow for the particles to bypass each other. Although single-file diffusion may play an important role in a wide range of industrial catalytic, geologic, and biological processes, experimental evidence is scarce despite the fact that the dynamics differ substantially from ordinary diffusion. We demonstrate the application of continuous-flow laser-polarized Xe-129 NMR spectroscopy for the study of gas transport into the effectively one-dimensional channels of a microporous material. The novel methodology makes it possible to monitor diffusion over a time scale of tens of seconds, often inaccessible by conventional NMR experiments. The technique can also be applied to systems with very small mobility factors or diffusion constants that are difficult to determine by currently available methods for diffusion measurement. Experiments using xenon in nanochannel systems can distinguish between unidirectional diffusion and single-file diffusion. The experimental observations indicate that single-file behavior for xenon in an organic nanochannel is persistent even at long diffusion times of over tens of seconds. Finally;using continuous flow laser-polarized Xe-129 NMR spectroscopy, we describe an intriguing correlation between the observed NMR line shape of xenon within the nanochannels and the gas transport into these channels.