We report the detection of a strong, organized magnetic field in the secondary component of the massive O8III/I+O7.5V/III double-lined spectroscopic binary system HD 47129 (Plaskett's star) in the context of the Magnetism in Massive Stars survey. Eight independent Stokes V observations were acquired using the Echelle SpectroPolarimetric Device for the Observations of Stars (ESPaDOnS) spectropolarimeter at the Canada–France–Hawaii Telescope and the Narval spectropolarimeter at the Télescope Bernard Lyot. Using least-squares deconvolution we obtain definite detections of signal in Stokes V in three observations. No significant signal is detected in the diagnostic null (N) spectra. The Zeeman signatures are broad and track the radial velocity of the secondary component; we therefore conclude that the rapidly rotating secondary component is the magnetized star. Correcting the polarized spectra for the line and continuum of the (sharp-lined) primary, we measured the longitudinal magnetic field from each observation. The longitudinal field of the secondary is variable and exhibits extreme values of −810 ± 150 and +680 ± 190 G, implying a minimum surface dipole polar strength of 2850 ± 500 G. In contrast, we derive an upper limit (3σ) to the primary's surface magnetic field of 230 G. The combination of a strong magnetic field and rapid rotation leads us to conclude that the secondary hosts a centrifugal magnetosphere fed through a magnetically confined wind. We revisit the properties of the optical line profiles and X-ray emission – previously interpreted as a consequence of colliding stellar winds – in this context. We conclude that HD 47129 represents a heretofore unique stellar system – a close, massive binary with a rapidly rotating, magnetized component – that will be a rich target for further study.