There is strong observational evidence that the 1999 MW 7.1 Hector Mine earthquake in the Mojave Desert, California, was triggered by the nearby 1992 MW 7.3 Landers earthquake. Many authors have proposed that the Landers earthquake directly stressed the Hector Mine fault. Our model of the Landers aftershock sequence, however, suggests there is an 85% chance that the Hector Mine hypocenter was actually triggered by a chain of smaller earthquakes that was initiated by the Landers main shock. We perform our model simulations using the Monte Carlo method based on the Gutenberg-Richter relationship, Omori's law, B¿th's law, and assumptions that all earthquakes, including aftershocks, are capable of producing aftershocks and that aftershocks produce their own aftershocks at the same rate that other earthquakes do. In general, our simulations show that if it has been more than several days since an M ≥ 7 main shock, most new aftershocks will be the result of secondary triggering. These secondary aftershocks are not physically constrained to occur where the original main shock increased stress. This may explain the significant fraction of aftershocks that have been found to occur in main shock stress shadows in static Coulomb stress triggering studies.