  We point out that the new exotic resonances recently reported by LHCb in the
$J/\psi p$ channel are excellent candidates for photoproduction off a proton
target. This test is crucial to confirming the resonant nature of such states,
as opposed to their being kinematical effects. We specialize to an
interpretation of the heavier narrow state as a molecule composed of $\Sigma_c$
and $\bar D^*$, and estimate its production cross section using vector
dominance. The relevant photon energies and fluxes are well within the
capabilities of the GlueX and CLAS12 detectors at Thomas Jefferson National
Accelerator Facility (JLAB). A corresponding calculation is also performed for
photoproduction of an analogous resonance which is predicted to exist in the
$\Upsilon p$ channel.
