Two of the strongest emission lines in the spectra of the planetary nebulae were identified by Boyce, Menzel and Payne (1) as due to forbidden transitions in the ground configuration of doubly ionized neon. The transitions are of wave-length 3967 and of wave-length 3869 in the configuration Ne III 1s22s22p4. These lines are excited by inelastic collisions of electrons with the neon ions. In order to investigate these transitions in detail a knowledge of the collision cross-sections is required. As a first step in this direction, wave functions have been calculated for the 3P state by the method of the self-consistent field, including the effect of exchange. In later papers these wave functions will be used in the calculation of collision cross-sections, in a study of the departures from the Landé rule in the triplets of the p2 and p4 configurations and, it is hoped, in the calculation of line strengths for certain permitted lines of astrophysical importance in the spectrum of Ne II.