The deposition of plasma in the central cell of a tandem mirror such as TMX has been calculated for gas box fueling, in which injected gas is confined to the thin fan of the quadrupole magnetic field. For TMX parameters the neutral density in the plasma center arises primarily from Franck-Condon atoms generated at the plasma edge. The fueling at the center is quite insensitive to the plasma parameters because the Franck-Condon mean free path is comparable to the plasma thickness.