  Materials that realize Kitaev spin models with bond-dependent anisotropic
interactions have long been searched for, as the resulting frustration effects
are predicted to stabilize novel forms of magnetic order or quantum spin
liquids. Here we explore the magnetism of $\gamma$-Li$_2$IrO$_3$, which has the
topology of a 3D Kitaev lattice of inter-connected Ir honeycombs. Using
resonant magnetic x-ray diffraction we find a complex, yet highly-symmetric
incommensurate magnetic structure with non-coplanar and counter-rotating Ir
moments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturally
accounts for all key features of the observed magnetic structure. Our results
provide strong evidence that $\gamma$-Li$_2$IrO$_3$ realizes a spin Hamiltonian
with dominant Kitaev interactions.
