The invention relates to a chimeric monomer-dimer hybrid protein wherein the protein comprises a first and a second polypeptide chain, the first polypeptide chain comprising at least a portion of an immunoglobulin constant region and a biologically active molecule, and the second polypeptide chain comprising at least a portion of an immunoglobulin constant region without the biologically active molecule of the first chain. The invention also relates to methods of using and methods of making the chimeric monomer-dimer hybrid protein of the invention.