The CH$^+$ ion is a key species in the initial steps of interstellar carbon chemistry. Its formation in diverse environments where it is observed is not well understood, however, because the main production pathway is so endothermic (4280 K) that it is unlikely to proceed at the typical temperatures of molecular clouds. We investigation CH$^+$ formation with the first velocity-resolved spectral mapping of the CH$^+$ $J=1-0, 2-1$ rotational transitions, three sets of CH $Lambda$-doubled triplet lines, $^{12}$C$^+$ and $^{13}$C$^+$, and CH$_3$OH 835~GHz E-symmetry Q branch transitions, obtained with Herschel/HIFI over $approx$12 arcmin$^2$ centered on the Orion BN/KL source. We present the spatial morphologies and kinematics, cloud boundary conditions, excitation temperatures, column densities, and $^{12}$C$^+$ optical depths. Emission from C$^+$, CH$^+$, and CH is indicated to arise in the diluted gas, outside of the explosive, dense BN/KL outflow. Our models show that UV-irradiation provides favorable conditions for steady-state production of CH$^+$ in this environment. Surprisingly, no spatial or kinematic correspondences of these species are found with H$_2$ S(1) emission tracing shocked gas in the outflow. We propose that C$^+$ is being consumed by rapid production of CO to explain the lack of C$^+$ and CH$^+$ in the outflow, and that fluorescence provides the reservoir of H$_2$ excited to higher ro-vibrational and rotational levels. Hence, in star-forming environments containing sources of shocks and strong UV radiation, a description of CH$^+$ formation and excitation conditions is incomplete without including the important --- possibly dominant --- role of UV irradiation.
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