V488 Persei is the most extreme debris disk known in terms of the fraction of the stellar luminosity it intercepts and reradiates. The infrared output of its disk is extremely variable, similar in this respect to the most variable disk known previously, that around ID8 in NGC 2547. We show that the variations are likely to be due to collisions of large planetesimals (≳100 km in diameter) in a belt being stirred gravitationally by a planetary or low-mass-brown-dwarf member of a planetary system around the star. The dust being produced by the resulting collisions is falling into the star due to drag by the stellar wind. The indicated planetesimal destruction rate is so high that it is unlikely that the current level of activity can persist for much longer than ~1000-10,000 yr and it may signal a major realignment of the configuration of the planetary system.