Diiodobutadiyne forms cocrystals with bis(pyridyl)oxalamides in which the diyne alignment is near the ideal parameters for topochemical polymerization to the ordered conjugated polymer, poly(diiododiacetylene) (PIDA). Nonetheless, previous efforts to induce polymerization in these samples via heat or irradiation were unsuccessful. We report here the successful ordered polymerization of diiodobutadiyne in these cocrystals, by subjecting them to high external pressure (0.3-10 GPa). At the lower end of the pressure range, the samples contain primarily monomer, as demonstrated by X-ray diffraction studies, but some polymerization does occur, leading to a pronounced color change from colorless to blue and to the development of intense Raman peaks at 962, 1394, and 2055 cm-1, corresponding to the poly(diacetylene). At higher pressures, the samples turn black and contain primarily polymer, as determined by solid-state NMR and Raman spectroscopy. Both density functional theory calculations (B3LYP/LanL2DZ) and comparisons to authentic samples of PIDA have confirmed the data analysis.