The origin and evolution of magnetism in OB stars is far from being well understood. With approximately 70 magnetic OB stars known, any new object with unusual characteristics may turn out to be a key piece of the puzzle. We report the detection of an exceptionally strong magnetic field in the He-strong B2IV star CPD -62° 2124. Spectropolarimetric FORS2 and HARPSpol observations were analysed by two independent teams and procedures, concluding on a strong longitudinal magnetic field of approximately 5.2 kG. The quantitative characterisation of the stellar atmosphere yields an effective temperature of 23 650 ± 250 K, a surface gravity of 3.95 ± 0.10 dex and a surface helium fraction of 0.35 ± 0.02 by number. The metal composition is in agreement with the cosmic abundance standard, except for Mg, Si and S, which are slightly non-solar. The strong and broad ( 300 km s-1) disc-like emission displayed by the Hα line suggests a centrifugal magnetosphere supported by the strong magnetic field. Our results imply that CPD -62° 2124 is an early B-type star hosting one of the strongest magnetic fields discovered to date, and one of the most evolved He-strong stars known, with a fractional main-sequence lifetime of approximately 0.6. Based on observations made with ESO telescopes at the La Silla and Paranal observatories under programme ID 191.D-0255(G,I).