One of the most intriguing scenarios proposed to explain how active galactic nuclei are triggered involves the existence of a supermassive binary black hole system in their cores. Here we present an observational evidence for the first spectroscopically resolved sub-parsec orbit of a such system in the core of Seyfert galaxy NGC 4151. Using a method similar to those typically applied for spectroscopic binary stars we obtained radial velocity curves of the supermassive binary system, from which we calculated orbital elements and made estimates about the masses of components. Our analysis shows that periodic variations in the light and radial velocity curves can be accounted for an eccentric, sub-parsec Keplerian orbit of a 15.9-year period. The flux maximum in the lightcurve correspond to the approaching phase of a secondary component towards the observer. According to the obtained results we speculate that the periodic variations in the observed H{alpha} line shape and flux are due to shock waves generated by the supersonic motion of the components through the surrounding medium. Given the large observational effort needed to reveal this spectroscopically resolved binary orbital motion we suggest that many such systems may exist in similar objects even if they are hard to find. Detecting more of them will provide us with insight into black hole mass growth process.