We report on the unconventional magnetism in the cubic B-site ordered double perovskite Ba2YMoO6, using ac and dc magnetic susceptibility, heat capacity and muon spin rotation. No magnetic order is observed down to 2 K while the Weiss temperature is ~-160K. This is ascribed to the geometric frustration in the lattice of edge-sharing tetrahedra with orbitally degenerate Mo5+ s=1/2 spins. Our experimental results point to a gradual freezing of the spins into a disordered pattern of spin singlets, quenching the orbital degeneracy while leaving the global cubic symmetry unaffected, and providing a rare example of a valence bond glass. © 2010 The American Physical Society.