We construct a novel topologically massive Abelian Chern-Simons gauge theory with 32 global supersymmetries in three space-time dimensions. In spite of the 32 supercharges, the theory exhibits massive excitations only up to spin 1. The possibility of such a multiplet shortening is due to the presence of noncentral R-symmetry generators in the Poincar\'e superalgebra, whose supermultiplets are determined.