The type of illumination used in museums is an important issue because of the damaging effects of light and because the visual impression of art works is critically influenced by the spectral profile and intensity of the illumination. The aim of this work was to determine computationally the spectrum of the illumination maximizing the number of colors perceived by normal observers when viewing art paintings. Hyperspectral images of eleven oil paintings were collected at the museum and the chromatic diversity under specific illuminants was estimated by computing the representation of the paintings in the CIELAB color space and by counting the number of nonempty unit cubes occupied by the corresponding color volume. An optimization algorithm was used to estimate the illuminant spectrum maximizing the number of colors for each painting. It was found that the optimized illuminant varied little with the painting and that it could produce a chromatic diversity about 25% higher than D₆₅. These results suggest that spectrally tuned light sources may improve appreciation of art paintings.