Muography consists in observing the differential absorption of muons - elementary particles produced through cosmic-ray interactions in the Earth atmosphere - going through the volcano and can attain a spatial resolution of tens of meters. We present here the first experiment of nuclear emulsion muography at the Stromboli volcano. Muons have been recorded during a period of five months by a detector of 0.96 m2 area. The emulsion films were prepared at the Gran Sasso underground laboratory and were analyzed at Napoli, Salerno and Tokyo scanning laboratories. Our results highlight a significant low-density zone at the summit of the volcano with density contrast of 30-40% with respect to bedrock. The structural setting of this part of the volcanic edifice controls the eruptive dynamics and the stability of the "Sciara del Fuoco" slope, which is affected by recurrent tsunamigenic landslides. Periodical imaging of the summit of the Stromboli volcano such as that provided by muography can become a useful method for studying the evolution of the internal structure of the volcanic edifice.