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In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)),which is an abstract algebraic object leading to rational solutions of theYang-Baxter equation on representations. We find that on the fundamentalrepresentation the universal R-matrix reduces to the standard rational R-matrixR = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared toprefactors one finds e.g. for sl(n) R-matrices. This leads precisely to theS-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory andtwo-loop N = 6 Chern-Simons theory.

Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry