  We report a Fermi-LAT $\gamma$-ray analysis for the Chamaeleon
molecular-cloud complex using a total column density (NH) model based on the
dust optical depth at 353 GHz ($\tau_{353}$) with the Planck thermal dust
emission model. Gamma rays with energy from 250 MeV to 100 GeV are fitted with
the NH model as a function of $\tau_{353}$, NH $\propto$
$\tau_{353}^{1/\alpha}$ ($\alpha$ $\geq$ 1.0), to explicitly take into account
a possible nonlinear $\tau_{353}$/NH ratio. We found that a nonlinear relation,
$\alpha$$\sim$1.4, gives the best fit to the $\gamma$-ray data. This nonlinear
relation may indicate dust evolution effects across the different gas phases.
Using the best-fit NH model, we derived the CO-to-H2 conversion factor (XCO)
and gas mass, taking into account uncertainties of the NH model. The value of
XCO is found to be (0.63-0.76) $\times$10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$
s, which is consistent with that of a recent $\gamma$-ray study of the
Chamaeleon region. The total gas mass is estimated to be (6.0-7.3) $\times$
10$^{4}$ Msun, of which the mass of additional gas not traced by standard HI or
CO line surveys is 20-40%. The additional gas amounts to 30-60% of the gas mass
estimated in the case of optically thin HI and has 5-7 times greater mass than
the molecular gas traced by CO. Possible origins of the additional gas are
discussed based on scenarios of optically thick HI and CO-dark H2. We also
derived the $\gamma$-ray emissivity spectrum, which is consistent with the
local HI emissivity derived from LAT data within the systematic uncertainty of
$\sim$20%
