  We investigate the interplay between the Kondo effect and randomness in
MxTiSe2 (M = Co, Ni, and Fe) single crystals. Although the typical low-T upturn
of resistivity implies the Kondo effect around the single-ion Kondo temperature
\overline{T}_{K}, positive magnetoresistance linearly proportional to the
magnetic field and the power-law scaling of magnetization suggest the forbidden
coexistence between Kondo effect and time reversal symmetry breaking. This
puzzling result is resolved by the Griffiths scenario - disorder-induced
distribution of the Kondo temperature produces an effective Kondo temperature
(\overline{T}_{K}) much lower than \overline{T}_{K}, allowing unscreened local
moments above \overline{T}_{K} and resulting in non-Fermi liquid properties in
MxTiSe2 below the percolation threshold (x<xc).
