  We demonstrate that amplitudes based on matter supermultiplets can be
combined to provide amplitudes of vector supermultiplets by means of KLT
relations. In practice we do this by developing a procedure for removing
supersymmetry supercharges from super Yang-Mills theory and supergravity
supermultiplets, reducing them to vector and chiral supermultiplets
respectively. This way, we reduce the super KLT relations to chiral KLT
relations making chiral squaring of amplitudes manifest. We study these chiral
KLT relations, discussing permutation symmetry and vanishing relations. Finally
some explicit calculations are done to show how the relations work in detail.
