We discuss the ground state of the spin-orbital model for spin-one ions with partially filled t2g levels on a honeycomb lattice. We find that the orbital degrees of freedom induce a spontaneous dimerization of spins and drive them into nonmagnetic manifold spanned by hard-core dimer (spinsinglet) coverings of the lattice. The cooperative "dimer Jahn-Teller" effect is introduced through a magnetoelastic coupling and is shown to lift the orientational degeneracy of dimers leading to a peculiar valence bond crystal pattern. The present theory provides a theoretical explanation of nonmagnetic dimerized superstructure experimentally seen in Li2RuO3 compound at low temperatures. The nearest-neighbor Heisenberg antiferromagnet on a bipartite lattice has a Néel-type magnetically long-range ordered ground state. However, such a classical order of spins can be destabilized by introducing a frustration into the system through the competing interactions that may lead to the extensively degenerate classical ground states [1]. In such systems exotic quantum phases without longrange order can emerge as the true ground states. In this Letter we want to point out and discuss another scenario, that can appear when magnetic ions on a bipartite lattice possess also an orbital degeneracy. The physics of such systems may be drastically different from that of pure spin models, as the occurrence of an orbital ordering can modulate the spin exchange and preclude the formation of magnetically ordered state on a bipartite lattice. In the following we focus on a system with threefold-orbitally-degenerate S = 1 magnetic ions on a honeycomb lattice. This model is suitable to describe d 2 and d 4 -type transition-metal compounds with partially filled t 2g levels, like the layered compound Li 2 RuO 3 [2]. Here the layers are formed by edge-sharing network of RuO 6 and LiO 6 octahedra. The Ru ions make a honeycomb lattice and Li ions reside in the centers of hexagons. These layers are well separated by the remaining Li ions. The magnetically active Ru 4+ -ions are characterized by four electrons in the threefold degenerate t 2g -manifold coupled into a S = 1 state. Li 2 RuO 3 undergoes a metalto-insulator transition on cooling below 540 K [2]. At the transition the magnetic susceptibility shows a steep decrease and its low temperature value can be considered to be due almost entirely to the Van Vleck paramagnetism. The structural analyses have revealed the formation of dimerized superstructure of Ru-Ru bonds in the low temperature phase. These observations indicate that Ruthenium spin-one degrees of freedom are mysteriously missing at low temperatures and suggest the formation of an unusual spin-singlet dimer phase in the ground state of the system.Here we describe the microscopic theory behind the stabilization of such a spin-singlet dimer state. We argue that, remarkably, such a novel phase can be realized on a honeycomb lattice because of orbital degeneracy, without invoking any exotic spin-only interactions. A possibility of formation of or...