A planar stationary and isotropic STIT tessellation at time t > 0 is observed in the window Wρ = t −1 √ π ρ · [− 1 2 , 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 Wρ as ρ goes to infinity.