  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-1/2
frustrated antiferromagnet. We investigate the role of quantum fluctuations as
the primary mechanism lifting the macroscopic degeneracy inherited by classical
spins on this lattice. In the semi-classical limit we predict, based on large-N
calculations, that an unusual $\vec q=0$ coplaner magnetically ordered ground
state is stabilized with no local "weather vane" modes. This phase melts in the
quantum limit and a gapped topological Z$_2$ spin liquid phase emerges. In the
vicinity of this quantum phase transition, we study the dynamic spin structure
factor and comment on the relevance of our results for future neutron
scattering experiments.
