The distribution of a random copolymer P(A(f)-r-B-1-f) at the interface between immiscible A and B phases as a function of the copolymer composition, denoted by the fraction f of A monomers, and as a function of the monomer-monomer interactions, or chi values, has been studied via lattice Monte Carlo simulations. A symmetric distribution of the copolymer was found for compositionally symmetric chains (f = 0.5) when the chi values were independent of the copolymer composition. In contrast, an asymmetric distribution of the copolymer was found for a compositionally asymmetric copolymer (f = 2/3) with composition-independent chi values. It was found that a symmetric distribution of the compositionally asymmetric copolymer can result only when the chi values are allowed to depend upon the copolymer composition. Such a symmetric distribution of a compositionally asymmetric copolymer is in qualitative agreement with miscibility, neutron reflectivity, and adhesion studies of polystyrene/poly(methyl methacrylate) systems.