The pressure-driven phase transformation from the sphalerite (B3) to rock salt (B1) crystal structures is studied in "constant stress" molecular dynamics simulations of ionic nanocrystals. Direct observation and calculated diffraction patterns confirm the transition. The mechanism is described and is shown to have consequences for the overall shape of the nanocrystals and in the formation of grain boundaries. The effects of pressurization rate and nanocrystal size on the transition pressure are discussed.