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⊙, 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 〈Bz〉, coupled with probable Zeeman splitting of the Stokes I profiles of metal lines confirming a surface field modulus 〈B〉 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*.