  Recent work has studied the growth of commutators as a probe of chaos and
information scrambling in quantum many-body systems. In this work we study the
effect of static disorder on the growth of commutators in a variety of
contexts. We find generically that disorder slows the onset of scrambling, and,
in the case of a many-body localized state, partially halts it. We access the
many-body localized state using a standard fixed point Hamiltonian, and we show
that operators exhibit slow logarithmic growth under time evolution. We compare
the result with the expected growth of commutators in both localized and
delocalized non-interacting disordered models. Finally, based on a scaling
argument, we state a conjecture about the effect of weak interactions on the
growth of commutators in an interacting diffusive metal.
