We report observations of an unpredicted fine structure in the activity profile of the Leonid meteor storm of 1999 November 18. Our observations were obtained at three widely separated sites (on the Iberian peninsula, in Germany, and in Northern Sweden) and with two totally different techniques (video cameras and meteor radars). The observations clearly show quasi-periodic variations of the meteor rate with temporal separations of individual maxima in the 6- to 9-min range. These temporal variations translate into spatial variations within the dust trail with scales between 10000 and 30000 km, depending in which reference frame or direction one chooses to compare. The times for the central three maxima as observed at the three sites agree within 2 min of each other after application of the appropriate topocentric time corrections. We consider a number of potential causes for the observed density variations within the meteor stream.