  Motivated by the intrinsic non-Fermi-liquid behavior observed in the
heavy-fermion quasicrystal $\mbox{Au}_{51}\mbox{Al}_{34}\mbox{Yb}_{15}$, we
study the low-temperature behavior of dilute magnetic impurities placed in
metallic quasicrystals. We find that a large fraction of the magnetic moments
are not quenched down to very low temperatures $T$, leading to a power-law
distribution of Kondo temperatures $P(T_{\mbox{K}})\sim
T_{\mbox{K}}^{\alpha-1}$, with a nonuniversal exponent $\alpha$, in a
remarkable similarity to the Kondo-disorder scenario found in disordered
heavy-fermion metals. For $\alpha<1$, the resulting singular $P(T_{\mbox{K}})$
induces non-Fermi-liquid behavior with diverging thermodynamic responses as
$T\rightarrow0$.
