  We propose to study the structure of the enigmatic $\chi_{c1}(3872)$ axial
vector meson through its $\gamma^*_L \gamma \to \chi_{c1}(3872)$ transition
form factor. We derive a light-front wave function representation of the form
factor for the lowest $c \bar c$ Fock-state. We found that the reduced width of
the state is well within the current experimental bound recently published by
the Belle collaboration. This strongly suggests a crucial role of the $c \bar
c$ Fock-state in the photon-induced production. Our results for the $Q^2$
dependence can be tested by future single tagged $e^+ e^-$ experiments, giving
further insights into the short-distance structure of this meson.
