  We report the discovery and analysis of a very strong magnetic field in the
rapidly rotating early B-type star HR 5907, based on observations obtained as
part of the Magnetism in Massive Stars (MiMeS) project. We infer a rotation
period of 0.508276 +0.000015/-0.000012 d from photometric and H{\alpha} EW
measurements, making this the shortest period, non-degenerate, magnetic massive
star known to date. From the comparison of IUE UV and optical spectroscopy with
LTE BRUCE/KYLIE models we find a solid-angle integrated, uniform black-body
temperature of 17 000 \pm 1000 K, a projected rotational velocity of 290 \pm 10
km/s, an equatorial radius of 3.1 \pm 0.2 R_sun, a stellar mass of 5.5 \pm 0.5
M_sun, and an inclination angle of the rotation axis to our line-of-sight of 70
\pm 10\circ. Our measurements of the longitudinal magnetic field, which vary
between -500 and -2000 G, phase coherently with the rotation period and imply a
surface dipole field strength of \sim15.7 kG. On the other hand, from fits to
mean Least-Squares Deconvolved Stokes V line profiles we infer a dipole field
strength of \sim10.4 kG. This disagreement may result from a magnetic
configuration more complex than our model, and/or from the non-uniform helium
surface abundance distribution. In either case we obtain a magnetic obliquity
nearly aligned with the rotation axis ({\beta} = 7+2/-1\circ). Our optical
spectroscopy also shows weak variability in carbon, silicon and nitrogen lines.
The emission variability in hydrogen Balmer and Paschen lines indicates the
presence of a dense, highly structured magnetosphere, interpreted as a
centrifugally supported, magnetically confined circumstellar disk.
