  Dynamical localization is one of the most startling manifestations of quantum
interference, where the evolution of a simple system is frozen out under a
suitably tuned coherent periodic drive. Here, we show that, although any
randomness in the interactions of a many body system kills dynamical
localization eventually, spectacular remnants survive even when the disorder is
strong. We consider a disordered quantum Ising chain where the transverse
magnetization relaxes exponentially with time with a decay time-scale $\tau$
due to random longitudinal interactions between the spins. We show that, under
external periodic drive, this relaxation slows down ($\tau$ shoots up) by
orders of magnitude as the ratio of the drive frequency $\omega$ and amplitude
$h_{0}$ tends to certain specific values (the freezing condition). If $\omega$
is increased while maintaining the ratio $h_0/\omega$ at a fixed freezing
value, then $\tau$ diverges exponentially with $\omega.$ The results can be
easily extended for a larger family of disordered fermionic and bosonic
systems.
