  When constructing a Wilson chain to represent a quantum impurity model, the
effects of truncated bath modes are neglected. We show that their influence can
be kept track of systematically by constructing an "open Wilson chain" in which
each site is coupled to a separate effective bath of its own. As a first
application, we use the method to cure the so-called mass-flow problem that can
arise when using standard Wilson chains to treat impurity models with
asymmetric bath spectral functions at finite temperature. We demonstrate this
for the strongly sub-Ohmic spin-boson model at quantum criticality where we
directly observe the flow towards a Gaussian critical fixed point.
