Results of present and previous measurements of the23Na NMR response, dc- and ac-magnetic susceptibilities and the specific heat ofNa2V3O7at low temperatures suggest that this material is close to a quantum critical point (QCP) atm0H¼0 T. The experimental datacan be explained by assuming that below 100 K the localizedVmagnetic momentsðS¼12Þform a collection of dimers, with a broaddistribution of singlet–triplet gaps. Most of the dimers adopt a singlet ground state with gaps between 0 and 350 K. A small fraction ofthem forms triplet ground states with gaps between 0 and 15 K. The degeneracy of the triplet ground states is lifted by a phase transitionat an unusually low temperature of 0.086 K. Modest magnetic fields effectively quench this low-temperature state and the system is drivenaway from the QCP as the applied fields are enhanced to above 1 T