We study the effect of strong disorder on the one-dimensional Kondo necklace model using a perturbative real-space renormalization group approach. The phase diagram of the model presents a random quantum critical point separating two phases; the random singlet phase of a quantum disordered XY chain and the random Kondo phase. We also consider an anisotropic version of the model which for strong disorder maps on the random transverse field Ising model. These results provide a microscopic basis for non-Fermi liquid behavior in disordered heavy fermions associated with the existence of Griffiths phases.

PACS numbers: 75.10.Hk, 64.60.Ak, 64.60.Cn