A detailed description is presented of the formation and removal processes of O+ ions in the upper atmosphere, and a model is constructed of the ion chemistry of the quiet ionsphere. The model is used in conjunction with the solar ultraviolet reference spectrum of Hinteregger and the Atmosphere Explorer C satellite data on the ion and electron temperatures and on the composition of the neutral atmosphere to predict the altitude profiles of the densities of O+, N+2, NO+, and O+2. The predicted ion densities are in harmony with the ion densities measured during representative mid-latitude daytime orbits by ion mass spectrometers carried aboard the Atmosphere Explorer C satillite.