  A planar stationary and isotropic STIT tessellation at time $t>0$ is observed
in the window $W_\rho={t^{-1}}\sqrt{\pi \ \rho}\cdot
[-\frac{1}{2},\frac{1}{2}]^2$, for $\rho>0$. 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 $W_\rho$ as $\rho$ goes to infinity.
