It is proposed to construct a far-detuned 3-dimensional optical lattice that can act as an atomic trap. Cooling of the atoms in the trap will be achieved by successive vibrational excitation and de-excitation in the vibrational wells set up by the optical waves. Once the atoms have been appropriately cooled, they will be used for precision measurements of atomic properties. In addition, vibrational cooling of two atoms at a single lattice site will be used as the starting point for the creation of cold, trapped molecules.