The first observation of the B0s→¯D0K0S decay mode and evidence for the B0s→¯D*0K0S decay mode are reported. The data sample corresponds to an integrated luminosity of 3.0  fb−1 collected in pp collisions by LHCb at center-of-mass energies of 7 and 8 TeV. The branching fractions are measured to be B(B0s→¯D0¯K0)=[4.3±0.5(stat)±0.3(syst)±0.3(frag)±0.6(norm)]×10−4,B(B0s→¯D*0¯K0)=[2.8±1.0(stat)±0.3(syst)±0.2(frag)±0.4(norm)]×10−4,where the uncertainties are due to contributions coming from statistical precision, systematic effects, and the precision of two external inputs, the ratio fs/fd and the branching fraction of B0→¯D0K0S, which is used as a calibration channel.