  Kondo impurities provide a nontrivial probe to unravel the character of the
excitations of a quantum spin liquid. In the S=1/2 Kitaev model on the
honeycomb lattice, Kondo impurities embedded in the spin-liquid host can be
screened by itinerant Majorana fermions via gauge-flux binding. Here, we report
experimental signatures of metallic-like Kondo screening at intermediate
temperatures in the Kitaev honeycomb material {\alpha}-RuCl3 with dilute Cr3+
(S=3/2) impurities. The static magnetic susceptibility, the muon Knight shift,
and the muon spin-relaxation rate all feature logarithmic divergences, a
hallmark of a metallic Kondo effect. Concurrently, the linear coefficient of
the magnetic specific heat is large in the same temperature regime, indicating
the presence of a host Majorana metal. This observation opens new avenues for
exploring uncharted Kondo physics in insulating quantum magnets.
