The possibility that an invisible solar companion passing through the Oort cloud every 28 Myr precipitates a sufficiently high rate of cometary collisions with the earth to account for periodic mass species extinctions recorded in the fossil record is discussed. A Monte Carlo simulation shows that any hypothesized 'death star' with a 28 Myr orbit would experience an average 10 percent change in period per orbit. Production of an 18-fold increase in cometary impacts would be associated with a 0.055 probability that a 10 km nucleus would hit the earth in a shower once every 510 Myr, longer than the proposed extinction periodicity. However, if the death star orbit has a 0.6 eccentricity and the Oort cloud is sufficiently densely populated, a 2 billion comet shower may be possible. A survey of large terrestrial impact craters indicates that 6-12 craters with diameters over 10 km originated in periodic showers. The extinctions in any case occur at 26 Myr periods and cannot be correlated with the 33 Myr period of recrossing the galactic plane, or with any other known phenomena.