We report the structural transformation of hexagonal Ba3YIr2O9 to a cubic double perovskite form (stable in ambient conditions) under an applied pressure of 8 GPa at 1273 K. While the ambient pressure synthesized sample undergoes long-range magnetic ordering at similar to 4 K, the high-pressure (HP) synthesized sample does not order down to 2 K as evidenced from our susceptibility, heat capacity, and nuclear magnetic resonance (NMR) measurements. Further, for the HP sample, our heat capacity data have the form gamma T + beta T-3 in the temperature (T) range of 2-10 K with the Sommerfeld coefficient gamma = 10 mJ/mol-Ir K-2. The Y-89 NMR shift has no T dependence in the range of 4-120 K and its spin-lattice relaxation rate varies linearly with T in the range of 8-45 K (above which it is T independent). Resistance measurements of both the samples confirm that they are semiconducting. Our data provide evidence for the formation of a 5d-based, gapless, quantum spin-liquid in the cubic (HP) phase of Ba3YIr2O9. In this picture, the gamma T term in the heat capacity and the linear variation of Y-89 1/T-1 arises from excitations out of a spinon Fermi surface. Our findings lend credence to the theoretical suggestion [Chen, Pereira, and Balents, Phys. Rev. B 82, 174440 (2010)] that strong spin-orbit coupling can enhance quantum fluctuations and lead to a QSL state in the double perovskite lattice.