  We report the discovery of large-amplitude, periodic X-ray emission from the
O7 V star theta^1 Orionis C, the central star of the Orion Nebula. Ten ROSAT
HRI snapshots of the Trapezium cluster taken over the course of 21 days show
that the count rate of theta^1 Ori C varies from 0.26 to 0.41 counts/s with a
clear 15-day period. The soft X-ray variations have the same phase and period
as H-alpha and He II 4686 variations reported by Stahl et al., and are in
anti-phase with the C IV and Si IV ultraviolet absorption features. We consider
five mechanisms which might explain the amplitude, phase, and periodicity of
the X-ray variations: (1) colliding-wind emission with an unseen binary
companion, (2) coronal emission from an unseen late-type pre-main--sequence
star, (3) periodic density fluctuations, (4) absorption of magnetospheric
X-rays in a corotating wind, and (5) magnetosphere eclipses. The ROSAT data
rule out the first three scenarios, but cannot rule out either of the latter
two which require the presence of an extended magnetosphere, consistent with
the suggestion of Stahl et al. that theta^1 Ori C is an oblique magnetic
rotator. As such, theta^1 Ori C may be the best example of a high-mass analog
to the chemically peculiar, magnetic Bp stars.
