Spin Liquid State in an Organic Mott Insulator with Triangular Lattice

${}^1$H NMR and static susceptibility measurements have been performed in an organic Mott insulator with nearly isotropic triangular lattice, $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$, which is a model system of frustrated quantum spins. The static susceptibility is described by the spin $S$ = 1/2 antiferromagnetic triangular-lattice Heisenberg model with the exchange constant $J$ $\sim$ 250 K. Regardless of the large magnetic interactions, the ${}^1$H NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is four-orders of magnitude smaller than $J$. These results suggest that a quantum spin liquid state is realized in the close proximity of the superconducting state appearing under pressure.