The results of experiments on chemical modification of viscous road asphalts with atactic polypropylene (APP) obtained by polymerization over a titanium–magnesium catalyst are presented. It has been shown that the preparation of an asphalt–polymer binder (APB) in an asphalt melt at 140°С is accompanied by the thermo-oxidative degradation of APP. The reaction scheme for chemical interaction of polyconjugated bitumen compounds with oxidized APP is presented. The APB materials with APP feature improved resistance to thermo-oxidative degradation and aging, high adhesion to mineral fillers, hardness, and heat resistance. A single-step technology for production of APB has been developed. The road concrete mixes with APP possess the lower water saturation and swelling in water, enhanced strength at 20 and 50°С, a low coefficient of heat sensitivity and enhanced crack resistance. The possibility of preparation of stone mastic asphalt (SMA) without admixture of specialty stabilizing fibrous additives has been experimentally proven.