This paper describes experimental studies of spontaneous imbibition of oil by water in a low-permeability outcrop chalk. At constant and high interfacial tension (IFT), the importance of capillary forces and the existence of a predominantly countercurrent mechanism were established. Additional experiments were performed to investigate the influence of length and of various boundary conditions. In another investigation, we modified the IFT at the sample boundary by using pairs of conjugate phases of the n-hexane/ethanol/brine ternary system. Final recovery increased when IFT was lowered. We give a numerical interpretation for this last result.