The transfer of protons involved in hydrogen bonding is fundamental to many chemical and biological processes. Quantum tunnelling can play an important role in this process(1,2). It manifests itself in strong isotope effects(3,4) and has been observed directly in the solid state(5). The tunnelling behaviour seen in such studies usually displays the characteristics of a particle confined in a double-well potential. But proton tunnelling can also occur in a coordinated fashion that involves many hydrogen bonds simultaneously. Such a process may significantly affect the properties of linear and circular networks of hydrogen bonds, which occur in ice and in macromolecules containing hydroxyl groups(6,7). Here we report the direct observation by NMR relaxometry of coordinated proton tunnelling in a cyclic array of four hydrogen bonds in solid p-tert-butyl calix[4]arene at low temperature. We are able to quantify the parameters that describe this phenomenon and find good agreement with theoretical predictions for phonon-assisted tunnelling(8).