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.
