Faraday rotation provides one of the most direct probes of magnetized plasma along the line of sight, from the large-scale Galactic magnetic field to compact plasma environments local to radio sources. In particular, temporal variations in rotation measure can trace changes in the density, magnetic-field strength, or geometry of the Faraday-rotating medium, as observed in radio pulsars and fast radio bursts. Long-period radio transients (LPTs), a recently identified class of coherent radio sources with periods of hundreds to thousands of seconds, remain poorly explored because their physical nature is still uncertain. Here we present full-Stokes observations of the 421-s LPT source CHIME J0630+25 and report, for the first time, extreme rotation measure (RM) variability from approximately -400 to -1630 rad m^-2. The rapid RM changes occur on short timescales, including a difference of approximately 50 rad m^-2 between two consecutive rotation periods and a sudden change of approximately 536 rad m^-2 within approximately 2500 s. Compared with other radio-emitting sources, CHIME J0630+25 occupies an unusual region of the DM-RM plane: despite its very small DM of approximately 22 pc cm^-3, |RM| reaches over 1.6 x 10^3 rad m^-2, far exceeding that expected from the interstellar medium and pulsars. The fast and large-amplitude RM variations should arise from a compact, structured, and rapidly evolving magneto-ionic environment local to the source, possibly associated with a compact binary system.