  The ground state of $\lambda$-(BEDT-TTF)$_2$GaCl$_4$, which has the same
structure as the organic superconductor $\lambda$-(BETS)$_2$GaCl$_4$, was
investigated by magnetic susceptibility and $^{13}$C NMR measurements. The
temperature dependence of the magnetic susceptibility revealed an
antiferromagnetic (AF) correlation with $J/k_{\rm B} \simeq$ 98 K. NMR spectrum
splitting and the divergence of $1/T_1$ were observed at approximately 13 K,
which is associated with the AF transition. We found that the AF structure is
commensurate according to discrete NMR peak splitting, suggesting that the
ground state of $\lambda$-(BEDT-TTF)$_2$GaCl$_4$ is an AF dimer-Mott insulating
state. Our results suggest that the superconducting phase of $\lambda$-type
salts would be located near the AF insulating phase.
