  We determine the magnetic field strength in the OMC 1 region of the Orion A
filament via a new implementation of the Chandrasekhar-Fermi method using
observations performed as part of the James Clerk Maxwell Telescope (JCMT)
B-Fields In Star-Forming Region Observations (BISTRO) survey with the POL-2
instrument. We combine BISTRO data with archival SCUBA-2 and HARP observations
to find a plane-of-sky magnetic field strength in OMC 1 of $B_{\rm
pos}=6.6\pm4.7$ mG, where $\delta B_{\rm pos}=4.7$ mG represents a
predominantly systematic uncertainty. We develop a new method for measuring
angular dispersion, analogous to unsharp masking. We find a magnetic energy
density of $\sim1.7\times 10^{-7}$ Jm$^{-3}$ in OMC 1, comparable both to the
gravitational potential energy density of OMC 1 ($\sim 10^{-7}$ Jm$^{-3}$), and
to the energy density in the Orion BN/KL outflow ($\sim 10^{-7}$ Jm$^{-3}$). We
find that neither the Alfv\'{e}n velocity in OMC 1 nor the velocity of the
super-Alfv\'{e}nic outflow ejecta is sufficiently large for the BN/KL outflow
to have caused large-scale distortion of the local magnetic field in the
$\sim$500-year lifetime of the outflow. Hence, we propose that the hour-glass
field morphology in OMC 1 is caused by the distortion of a primordial
cylindrically-symmetric magnetic field by the gravitational fragmentation of
the filament and/or the gravitational interaction of the BN/KL and S clumps. We
find that OMC 1 is currently in or near magnetically-supported equilibrium, and
that the current large-scale morphology of the BN/KL outflow is regulated by
the geometry of the magnetic field in OMC 1, and not vice versa.
