This paper presents a setup capable of producing a high-flux continuous beam of cold rubidium atoms for cavity quantum electrodynamics experiments in the region of strong coupling. A 2D(+) magneto-optical trap (MOT), loaded with rubidium getters in a dry-film-coated vapor cell, fed a secondary moving-molasses MOT (MM-MOT) at a rate greater than 2 x 10(10) atoms/s. The MMMOT provided a continuous beam with a tunable velocity. This beam was then directed through the waist of a cavity with a length of 280 A mu m, resulting in a vacuum Rabi splitting of more than +/- 10 MHz. The presence of a sufficient number of atoms in the cavity mode also enabled splitting in the polarization perpendicular to the input. The cavity was in the strong coupling region, with an atom-photon dipole coupling coefficient g of 7 MHz, a cavity mode decay rate kappa of 3 MHz, and a spontaneous emission decay rate gamma of 6 MHz.