  The production of a single charged Higgs boson pair by photon - photon
interactions in $pp$ collisions at the LHC is investigated in this exploratory
study. We focus on the exclusive production, which is characterized by intact
protons and two - rapidity gaps in the final state, and assume the type - I two
- Higgs - doublet model, which still allows a light charged Higgs. Assuming the
leptonic $H^{\pm}\rightarrow [\tau\nu_{\tau}]$ decay mode, we derive
predictions for the transverse momentum, rapidity and invariant mass
distributions of the $\tau^+ \tau^-$ pair for different values of the charged
Higgs mass. The contributions of different background processes are also
estimated. Our results indicate that the contribution of the exclusive $H^+
H^-$ production for the $[\tau^{+}\nu_{\tau}][\tau^{-} \nu_{\tau}]$ final state
is non - negligible and can, in principle, be used to searching for a light
charged Higgs.
