  The recently discovered three-dimensional hyperhoneycomb iridate,
$\beta$-Li$_2$IrO$_3$, has raised hopes for the realization of dominant Kitaev
interaction between spin-orbit entangled local moments due to its near-ideal
lattice structure. If true, this material may lie close to the sought-after
quantum spin liquid phase in three dimensions. Utilizing ab-initio electronic
structure calculations, we first show that the spin-orbit entangled basis,
$j_{\rm eff}$=1/2, correctly captures the low energy electronic structure. The
effective spin model derived in the strong coupling limit supplemented by the
ab-initio results is shown to be dominated by the Kitaev interaction. We
demonstrated that the possible range of parameters is consistent with a
non-coplanar spiral magnetic order found in a recent experiment. All of these
analyses suggest that $\beta$-Li$_2$IrO$_3$ may be the closest among known
materials to the Kitaev spin liquid regime.
