  ${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of
Klebanov et.al spontaneously breaks chiral symmetry in Minkowski space-time. We
demonstrate that in de Sitter space-time the chiral symmetry breaking occurs
for the values of the Hubble constant $H\lesssim 0.7 \Lambda $, as well as in a
narrow window $0.92(1) \Lambda \le H\le 0.92(5) \Lambda $. We give a precise
definition of the strong coupling scale $\Lambda $ of cascading gauge theory,
which is related to the glueball mass scale in the theory $m_{glueball}$ and
the asymptotic string coupling $g_s$ as $\Lambda \sim g_s^{1/2} m_{glueball}$.
