The first observation of the suppressed semileptonic B0sK+ decay is reported. Using a data sample recorded in pp collisions in 2012 with the LHCb detector, corresponding to an integrated luminosity of 2 fb1, the branching fraction B(B0sK+) is measured to be [1.06±0.05(stat)±0.08(syst)]×104, where the first uncertainty is statistical and the second one represents the combined systematic uncertainties. The decay B0sDs+, where Ds is reconstructed in the final state K+K, is used as a normalization channel to minimize the experimental systematic uncertainty. Theoretical calculations on the form factors of the B0sK and B0sDs transitions are employed to determine the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements |Vub|/|Vcb| at low and high B0sK momentum transfer.
