  HD 156324 is an SB3 (B2V/B5V/B5V) system in the Sco OB4 association. The
He-strong primary possesses both a strong magnetic field, and H$\alpha$
emission believed to originate in its Centrifugal Magnetosphere (CM). We
analyse a large spectroscopic and high-resolution spectropolarimetric dataset.
The radial velocities (RVs) indicate that the system is composed of two
sub-systems, which we designate A and B. Period analysis of the RVs of the
three components yields orbital periods $P_{\rm orb} = 1.5806(1)$~d for the Aa
and Ab components, and 6.67(2)~d for the B component, a PGa star. Period
analysis of the longitudinal magnetic field \bz~and H$\alpha$ equivalent
widths, which should both be sensitive to the rotational period $P_{\rm rot}$
of the magnetic Aa component, both yield $\sim$1.58~d. Since $P_{\rm orb} =
P_{\rm rot}$ Aa and Ab must be tidally locked. Consistent with this, the orbit
is circularized, and the rotational and orbital inclinations are identical
within uncertainty, as are the semi-major axis and the Kepler corotation
radius. The star's H$\alpha$ emission morphology differs markedly from both
theoretical and observational expectations in that there is only one, rather
than two, emission peaks. We propose that this unusual morphology may be a
consequence of modification of the gravitocentrifugal potential by the presence
of the close stellar companion. We also obtain upper limits on the magnetic
dipole strength $B_{\rm d}$ for the Ab and B components, respectively finding
$B_{\rm d} < 2.6$~kG and $<0.7$~kG.
