A simple method has been developed for growing low cost and large area CuInSe2 thin films, by close-spaced vapour transport in a vertical closed tube. A thermodynamical study of the system was carried out : the transport rate was measured as a function of the source and substrate temperatures, and compared to a model governed by either the diffusion or the reaction kinetics. With our experimental conditions, the growth rate is limited by the reaction kinetics, not by the diffusion. Nearly stoichiometric films were grown at temperatures as low as 350 degrees C, with deposition rates of 0.5 mu n min(-1) and grain sizes of the order of 1 mu m. Above 600 degrees C, the films are composed of (In,Se) compounds, mainly In2Se3.