  We develop a diagrammatic Monte Carlo method for the real-time dynamics of
dissipative quantum impurity models. These are small open quantum systems with
interaction and local Markovian dissipation, coupled to a large quantum bath.
  Our algorithm sample the hybridization expansion formulated on a single
real-time contour, rather than on the double Keldysh one, as it naturally
arises in the thermofield/vectorized representation of the Lindblad dynamics.
We show that local Markovian dissipation generally helps the convergence of the
diagrammatic Monte Carlo sampling by reducing the sign problem, thus allowing
to reach longer time scales as compared to the conventional unitary case. We
apply our method to an Anderson impurity model in presence of local dephasing
and discuss its effect on the charge and spin dynamics of the impurity.
