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Materials that realize Kitaev spin models with bond-dependent anisotropicinteractions have long been searched for, as the resulting frustration effectsare predicted to stabilize novel forms of magnetic order or quantum spinliquids. Here we explore the magnetism of $\gamma$-Li$_2$IrO$_3$, which has thetopology of a 3D Kitaev lattice of inter-connected Ir honeycombs. Usingresonant magnetic x-ray diffraction we find a complex, yet highly-symmetricincommensurate magnetic structure with non-coplanar and counter-rotating Irmoments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturallyaccounts for all key features of the observed magnetic structure. Our resultsprovide strong evidence that $\gamma$-Li$_2$IrO$_3$ realizes a spin Hamiltonianwith dominant Kitaev interactions.

Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3