This paper presents a first observational investigation of the faint Of?p star NGC 1624-2, yielding important new constraints on its spectral and physical characteristics, rotation, magnetic field strength, X-ray emission and magnetospheric properties. Modelling the spectrum and spectral energy distribution, we conclude that NGC 1624-2 is a main-sequence star of mass M ≃ 30 M&sun;, and infer an effective temperature of 35 ± 2 kK and log g = 4.0 ± 0.2. Based on an extensive time series of optical spectral observations we report significant variability of a large number of spectral lines, and infer a unique period of 157.99 ± 0.94 d which we interpret as the rotational period of the star. We report the detection of a very strong (5.35 ± 0.5 kG) longitudinal magnetic field , coupled with probable Zeeman splitting of the Stokes I profiles of metal lines confirming a surface field modulus of 14 ± 1 kG, consistent with a surface dipole of polar strength ≳20 kG. This is the largest magnetic field ever detected in an O-type star, and the first report of Zeeman splitting of Stokes I profiles in such an object. We also report the detection of reversed Stokes V profiles associated with weak, high-excitation emission lines of O III, which we propose may form in the close magnetosphere of the star. We analyse archival Chandra ACIS-I X-ray data, inferring a very hard spectrum with an X-ray efficiency of log Lx/Lbol = -6.4, a factor of 4 larger than the canonical value for O-type stars and comparable to that of the young magnetic O-type star θ1 Ori C and other Of?p stars. Finally, we examine the probable magnetospheric properties of the star, reporting in particular very strong magnetic confinement of the stellar wind, with η* ≃ 1.5 × 104, and a very large Alfvén radius, RAlf = 11.4 R*. Based on spectropolarimetric observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers (INSU) of the Centre National de la Recherche Scientifique of France, and the University of Hawaii, as well as on observations obtained using the Narval spectropolarimeter at the Observatoire du Pic du Midi (France), which is operated by the INSU. The spectroscopic data were gathered with five facilities: the 9.2-m Hobby-Eberly Telescope at McDonald Observatory (MDO), the 3.5-m Telescope at Calar Alto Observatory (CAHA), the 1.5-m Telescope at the Observatorio de Sierra Nevada (OSN), the 4.2-m William Herschel Telescope at the Observatorio del Roque de los Muchachos (ORM) and the 2-m Himalayan Chandra Telescope at Indian Astronomical Observatory (IAO).