The inspection of very large or thick structures represents one of the biggest challenges for nondestructive techniques. For such objects, a particularly powerful technique is muography, which makes use of free, natural cosmic-ray muons. Among other applications, this technique has been applied to provide two-dimensional (2D) images of nuclear reactors, pyramids, or volcanos. Recently, 3D algorithms developed for medical applications were adapted to the special case of muon imaging to derive density maps. The main difficulties relate to the size of the object and to the limited number of available projections. Here, we report on the first 3D imaging of a whole nuclear reactor, obtained without any prior information on its structure and using the largest set of muographic projections ever made in this field.