When linear polymer chains in dilute solution are subject to extensional flow, each chain in the sample experiences the coil-stretch transition at a different time. Using Brownian dynamics simulation, we have studied the distribution of transition times in terms of the extensional rate and the length of the chains. If instead of time one characterizes the effect of the flow by the accumulated strain, then the distribution and its moments seem to take general forms, independent of molecular weight and flow rate, containing some numerical, universal constants that have been evaluated from the dynamical simulation. The kinetics of the transition, expressed by the time-dependence of the fraction of remaining coils, has also been simulated, and the results for the kinetic rate constant has been rationalized in a manner similar to that used for the transition time. The molecular individualism, characterized in this work by the distribution of transition times, is related to the excess of the applied extensional rate over its critical value, which will determine the transition time and other features of the coil-stretch transition.