  We produce an ultracold and dense sample of rovibronic ground state Cs_2
molecules close to the regime of quantum degeneracy, in a single hyperfine
level, in the presence of an optical lattice. The molecules are individually
trapped, in the motional ground state of an optical lattice well, with a
lifetime of 8 s. For preparation, we start with a zero-temperature atomic
Mott-insulator state with optimized double-site occupancy and efficiently
associate weakly-bound dimer molecules on a Feshbach resonance. Despite
extremely weak Franck-Condon wavefunction overlap, the molecules are
subsequently transferred with >50% efficiency to the rovibronic ground state by
a stimulated four-photon process. Our results present a crucial step towards
the generation of Bose-Einstein condensates of ground-state molecules and, when
suitably generalized to polar heteronuclear molecules such as RbCs, the
realization of dipolar many-body quantum-gas phases in periodic potentials.
