  Tree-level scattering amplitudes in planar N=4 super Yang-Mills are known to
be Yangian-invariant. It has been shown that integrability allows to obtain a
general, explicit method to find such invariants. The uplifting of this result
to the amplituhedron construction has been an important open problem. In this
paper, with the help of methods proper to integrable theories, we successfully
fill this gap and clarify the meaning of Yangian invariance for the tree-level
amplituhedron. In particular, we construct amplituhedron volume forms from an
underlying spin chain. As a by-product of this construction, we also propose a
novel on-shell diagrammatics for the amplituhedron.
