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Recent experiments on the "hyper-kagome" lattice system Na$_4$Ir$_3$O$_8$have demonstrated that it is a rare example of a three dimensional spin-1/2frustrated antiferromagnet. We investigate the role of quantum fluctuations asthe primary mechanism lifting the macroscopic degeneracy inherited by classicalspins on this lattice. In the semi-classical limit we predict, based on large-Ncalculations, that an unusual $\vec q=0$ coplaner magnetically ordered groundstate is stabilized with no local "weather vane" modes. This phase melts in thequantum limit and a gapped topological Z$_2$ spin liquid phase emerges. In thevicinity of this quantum phase transition, we study the dynamic spin structurefactor and comment on the relevance of our results for future neutronscattering experiments.

Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8