We determined the crystal structure of Ba2CoSi2O6Cl2, which was synthesized in this work, and investigated its quantum magnetic properties using single crystals. This compound should be described as a two-dimensionally coupled spin-1 /2 XY-like spin dimer system. Ba2CoSi2O6Cl2 exhibits a stepwise magnetization process with a plateau at half of the saturation magnetization, irrespective of the field direction, although all the Co2+ sites are equivalent. This indicates that spin triplets are localized owing to the almost perfect frustration of interdimer exchange interactions. Thus, the spin states for the zero and 1/2 magnetization-plateau states are almost exactly given by the simple product of singlet dimers and the alternate product of singlet and triplet dimers, respectively.