Context. Since the discovery of its dusty disk in 1984, β Pictoris has become the prototype of young early-type planetary systems, and there are now various indications that a massive Jovian planet is orbiting the star at ∼10 AU. However, no planets have been detected around this star so far. Aims. Our goal was to investigate the close environment of β Pic, searching for planetary companion(s). Methods. Deep adaptive-optics L -band images of β Pic were recorded using the NaCo instrument at the Very Large Telescope. Results. A faint point-like signal is detected at a projected distance of 8 AU from the star, within the northeastern extension of the dust disk. Various tests were made to rule out possible instrumental or atmospheric artefacts at a good confidence level. The probability of a foreground or background contaminant is extremely low, based in addition on the analysis of previous deep HST images. Its L = 11.2 apparent magnitude would indicate a typical temperature of ∼1500 K and a mass of ∼8 M Jup . If confirmed, it could explain the main morphological and dynamical peculiarities of the β Pic system. The present detection is unique among A-stars by the proximity of the resolved planet to its parent star. Its closeness and location inside the β Pic disk suggest a formation process by core accretion or disk instabilities rather than binary-like formation processes.