In this letter, we present the Parkes-Siegel formulation for the massi
ve Abelian N = 1 super-QED(2+2) coupled to a self-dual supermultiplet,
by introducing a chiral multiplier superfield. We show that after car
rying out a suitable dimensional reduction from (2 + 2) to (1 + 2) dim
ensions, and performing some necessary truncations, the simple supersy
mmetric extension of the tau(3)QED(1+2) coupled to a Chem-Simons term
naturally comes out.