  We establish an all-loop conformal Yangian symmetry for the full set of
planar amplitudes in the recently proposed integrable bi-scalar field theory in
four dimensions. This chiral theory is a particular double scaling limit of
gamma-twisted weakly coupled N=4 SYM theory. Each amplitude with a certain
order of scalar particles is given by a single fishnet Feynman graph of disc
topology cut out of a regular square lattice. The Yangian can be realized by
the action of a product of Lax operators with a specific sequence of
inhomogeneity parameters on the boundary of the disc. Based on this
observation, the Yangian generators of level one for generic bi-scalar
amplitudes are explicitly constructed. Finally, we comment on the relation to
the dual conformal symmetry of these scattering amplitudes.
