  We discover a novel localization transition that alters the dynamics of
coherence in disordered many-body spin systems subject to Markovian
dissipation. The transition occurs in the middle spectrum of the Lindbladian
super-operator whose eigenstates obey the universality of non-Hermitian
random-matrix theory for weak disorder and exhibit localization of off-diagonal
degrees of freedom for strong disorder. This Lindbladian many-body localization
prevents many-body decoherence due to interactions and is conducive to
robustness of the coherent dynamics characterized by the rigidity of the decay
rate of coherence.
