IRAS has detected dust trails in the orbit of short-period comets but has been unable to detect such trails in the orbit of long-period comets. We now present observations from the study of a meteor outburst that identify the event as being due to just that. Ten orbits of meteoroids were measured during a brief but intense outburst of the α Monocerotid shower that confirm the theory that a trail of dust is brought occasionally in collision with the Earth by planetary perturbations. Observations of this event by multiple meteor observing techniques provide the first direct measurement of the size distribution of dust in a comet dust trail, the dust density in the trail of a long-period comet, and a cross section of such a trail in the path of Earth. The implication for detecting potential Earth-threatening long-period comets by their meteoric signature is discussed.