We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba_{3}ZnIr_{2}O_{9} is a realization of a novel spin-orbital liquid state. Our results reveal that Ba_{3}ZnIr_{2}O_{9} with Ir^{5+} (5d^{4}) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J=0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir_{2}O_{9} dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.