Neutron spectroscopy has revealed a highly unusual magnetic structure and dynamics in YVO3, an insulating pseudocubic perovskite that undergoes a series of temperature-induced phase transitions between states with different spin and orbital ordering patterns. A good description of the neutron data is obtained by a theoretical analysis of the spin and orbital correlations of a quasi-one-dimensional model. This leads to the tentative identification of one of the phases of YVO3 with the "orbital Peierls state," a theoretically proposed many-body state comprised of orbital singlet bonds.