The Treacy system, consisting of a pair of parallel transmissive diffraction gratings, is ordinarily used as a dispersion delay line for ultrashort laser pulses. The layer of free space bounded by these gratings represents the simplest isoplanar (invariant with respect to spatial shift) optical system. The pulse width in the region of the spatial chirp of the Treacy system is investigated, using the theory of isoplanar optical systems.