A planar stationary and isotropic STIT tessellation at time $t>0$ is observed in the window $W_ρ={t^{-1}}\sqrt{π\ ρ}\cdot [-\frac{1}{2},\frac{1}{2}]^2$, for $ρ>0$. With each cell of the tessellation, we associate the inradius, which is the radius of the largest disk contained in the cell. Using the Chen-Stein method, we compute the limit distributions of the largest order statistics for the inradii of all cells whose nuclei are contained in $W_ρ$ as $ρ$ goes to infinity.