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 ^ { -1 } , an equatorial radius of 3.1 \pm 0.2 R _ { \odot } , a stellar mass of 5.5 \pm 0.5 M _ { \odot } , and an inclination angle of the rotation axis to our line-of-sight of 70 \pm 10 \degr . 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 \sim 15.7 kG . On the other hand , from fits to mean Least-Squares Deconvolved Stokes V line profiles we infer a dipole field strength of \sim 10.4 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 } \degr ) . 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 .