  The possibility of a light charged Higgs boson $H^\pm$ that decays
predominantly to quarks ($cs$ and/or $cb$) and with a mass in the range 80 GeV
$\le m_{H^\pm} \le 90$ GeV is studied in the context of Three-Higgs-Doublet
Models (3HDMs). At present the Large Hadron Collider (LHC) has little
sensitivity to this scenario, and currently the best constraints are from LEP2
and Tevatron searches. The branching ratio of $H^\pm\to cb$ can be dominant in
two of the five types of 3HDM, and we determine the parameter space where this
occurs. The decay $H^\pm\to cb$ has recently been searched for at the LHC for
the first time, and with increased integrated luminosity one would expect
sensitivity to the region 80 GeV $\le m_{H^\pm} \le 90$ GeV due to the smaller
backgrounds with respect to $H^\pm\to cs$ decays.
