Peptide chain formation from amino acids such as glycine is a key step in the emergence of life. Unlike their synthesis by living systems, how peptide chains grow under abiotic conditions is an open question given the variety of organic compounds discovered in various astrophysical environments, comets and meteorites. We propose a new abiotic route in the presence of protonated molecular dimers of glycine in a cold gaseous atmosphere without further need for a solid catalytic substrate. The results provide evidence for the preferential formation of mixed protonated dimers of glycine consisting of a dipeptide and a glycine molecule instead of pure protonated glycine dimers. Additional measurements mimicking a cosmic-ray impact in terms of internal excitation show that a single gas-phase collision induces polymerization via dehydration in both the mixed and pure dimer ions. Peptide chain growth is thus demonstrated to occur via a unimolecular gas-phase reaction in an excited cluster ion.