The invention relates to a chimeric monomer-dimer hybrid protein that 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 polypeptide chain. The invention also relates to methods of using and methods of making the chimeric monomer-dimer hybrid protein of the invention.