This paper investigates the dynamics of a length of chain that is attached to the ocean floor, initially oriented vertically and the top end allowed to fall. A series of simulations of the falling was performed using a continuum model of the chain. It was found that, although initially the chain does fall straight down, when its speed approaches terminal velocity in this direction, it develops instabilities which cause severe motions in the chain, particularly at the top end of the chain. It was found that these motions are sensitive to the longitudinal drag coefficient, Cd,L . A statistical analysis of many different simulations of the falling process indicates that the whipping of the top end of the chain may be more dangerous to neighboring platforms or equipment than the impact of the chain on the bottom.