  We study a lattice realization of a Luttinger liquid interacting with a bath
of quantum spins in terms of an antiferromagnetic S=1/2 Heisenberg chain, where
each spin is also coupled to a \sigma=1/2 Kondo spin degree of freedom. This
model describes the low-energy spin dynamics in quasi one dimensional
materials, where the electronic spins of the magnetic ions interact with those
of impurities, nuclei and possibly other spin species present in their
environment. For large ferromagnetic and antiferromagnetic Kondo interaction J'
there are two phases corresponding to an effective spin-1 Heisenberg chain and
a dimerised spin-1/2 ladder, respectively. For weak Kondo interaction we
establish that the Kondo interaction drives the system to a strong coupling
regime. This suggests that J'=0 is the only critical point in the system.
