  We construct the Lax-pair, the classical monodromy matrix and the
corresponding solution of the Yang--Baxter equation, for a two-parameter
deformation of the Principal chiral model for a simple group. This deformation
includes as a one-parameter subset, a class of integrable gauged WZW-type
theories interpolating between the WZW model and the non-Abelian T-dual of the
principal chiral model. We derive in full detail the Yangian algebra using two
independent methods: by computing the algebra of the non-local charges and
alternatively through an expansion of the Maillet brackets for the monodromy
matrix. As a byproduct, we also provide a detailed general proof of the Serre
relations for the Yangian symmetry.
