The field sweep rate (v=dH/dt) and temperature (T) dependence of the magnetization reversal of a single-chain magnet (SCM) is studied at low temperatures. As expected for a thermally activated process, the nucleation field (H_n) increases with decreasing T and increasing v. The set of H_n(T,v) data is analyzed with a model of thermally activated nucleation of magnetization reversal. Below 1 K, H_n becomes temperature independent but remains strongly sweep rate dependent. In this temperature range, the reversal of the magnetization is induced by a quantum nucleation of a domain wall that then propagates due to the applied field.