We study the low-energy sector of the Heisenberg Necklace model. Using the field theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spins dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO 2 and Sr 2 CuO 3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the inchain exchange coupling, J. We consider the perturbation of the energy spectrum caused by the interaction, γ, with nuclear spins (I = 3/2) present on the same sites. We find that the resulting Necklace model has a characteristic energy scale, Λ ∼ J 1/3 (γI) 2/3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field, B. For µ B B > Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, √ 2 + 1.