  We report the existence of a phase transition at high temperature in the 3D
Kitaev candidate material, $\beta$-Li$_2$IrO$_3$. We show that the transition
is bulk, intrinsic and orders a tiny magnetic moment with a spatially
anisotropic saturation moment. We show that even though this transition is
global, it does not freeze the local Ir moments, which order at much lower
temperatures into an incommensurate state. Rather, the ordered moment has an
orbital origin that is coupled to spin correlations, likely of a Kitaev origin.
The separate ordering of spin-correlated orbital moments and of local Ir
moments reveals a novel way in which magnetic frustration in Kitaev systems can
lead to coexisting magnetic states.
