  We study the low-temperature properties of a one-dimensional spin-1/2 chain
of magnetic impurities coupled to a (normal) metal environment by means of
anisotropic Kondo exchange. In the case of easy-plane anisotropy, we obtain the
phase diagram of this system at T=0. We show that the in-plane Kondo coupling
destabilizes the Tomonaga-Luttinger phase of the spin-chain, and leads to two
different phases: i) At strong Kondo coupling, the spins in the chain form
Kondo singlets and become screened by the metallic environment, and ii) At weak
and intermediate Kondo coupling, we find a novel dissipative phase
characterized by diffusive gapless spin excitations. The two phases are
separated by a quantum critical point of the Wilson-Fisher universality class
with dynamical exponent $z\simeq2$.
