The total cross section ${\ensuremath{\sigma}}_{T}$ for orthopositronium (o-Ps) scattering from argon gas has been measured directly for the first time using a variable energy o-Ps beam in the range 16--95 eV. The cross section is found to rise from a value of approximately $9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ to $15\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{m}}^{2}$ in the 16--30 eV range and thereafter decline slowly to $11\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{m}}^{2}$ at the highest energy investigated. Comparison with theory suggests that the increase in ${\ensuremath{\sigma}}_{T}$ is probably due to inelastic processes.