3C 84 (NGC 1275, Perseus A) is a bright radio source at the center of an ongoing merger, where HST observations show two colliding spiral galaxies. 3C 84 holds promise to improve our understanding about how of the activity of active galactic nuclei, the formation of supermassive binary black holes, feedback processes, and galaxy collisions are interrelated. 3C,84 is one of only six radio galaxies, which reveal TeV emission. The origin of this TeV emission is still a matter of debate. Our present study is based on high resolution radio interferometric observations (15 GHz) of the pc-scale jet in this complex radio galaxy. We have re-modeled and re-analyzed 42 VLBA observations of 3C 84, performed between 1999.99 and 2017.65. In order to enable a proper alignment of the VLBA observations, we developed a method of a “differential” alignment whereby we select one reference point and minimize the deviations from this reference point in the remaining epochs. As a result, we find strong indication for a precession of the 3C 84 jet—not only for its central regions, but also for the outer lobe at 10 mas distance. These findings are further supported by our kinematic precession modeling of the radio flux-density monitoring data provided by the University of Michigan Radio Observatory and the Owens Valley Radio Observatory, which yields a precession time scale of about 40 yr. This time scale is further supported by literature maps obtained about 40 yr ago (1973 and 1974.1) which reveal a similar central radio structure. We suggest that the TeV flare detected by MAGIC may correlate with the precession of 3C 84, as we disentangle a projected reversal point of the precessing motion that correlates with the flaring time. This may physically be explained by a precessing jet sweeping over a new region of so far undisturbed X-ray gas which would then lead to shock-produced TeV-emission. In addition, we perform a correlation analysis between the radio data and GeV data obtained by the Fermi Gamma-ray Space Telescope and find that the γ -ray data are lagging the radio data by 300–400 days. A possible explanation could be that the radio and the GeV data stem from different emission regions. We discuss our findings and propose that the detected jet precession can also account for the observed cavities in the X-ray emission on kpc-scales.