Crystalline solids composed of one-dimensional channels with cross-sectional dimensions below 1 nm represent an intriguing class of materials with important potential applications. A key characteristic for certain applications is the average open channel persistence length, i.e., the ensemble average distance from a channel opening to the first obstruction. This paper introduces an NMR-based methodology to measure this quantity. The protocol is applied to polycrystalline specimens of two different dipeptide nanotubes: l-Ala-l-Val and its retro-analog l-Val-l-Ala. Persistence lengths derived from the NMR measurements are found to be comparable to the typical crystallite dimensions seen in scanning electron microscopy (SEM) images, indicating that the crystals of these AV and VA specimens are essentially hollow with practically no blockages. Applications of the method to an AV sample that has been pulverized in a mortar and pestle showed that the open channel persistence length was reduced from 50 to 6.6 μm, consistent with the crystallite sizes observed in SEM images.