The problem of the close packing of spheres is investigated exhaustively for the case in which the spheres occupy the lattice points of a space lattice. This type of packing can be realized in boxes with plane walls as suggested by Langmuir and Nelson. It is shown that there are fifteen types of packing which differ from one another either in symmetry or in the number of contacts a given sphere makes with its neighbors. In these fifteen types, ten of the fourteen Bravais lattices are represented. The use of lattice close packing as a basis for models of more complex structures is discussed.