Using a constant "velocity gradient'' ensemble approach, the average scalar end-to-end separation is calculated as a function of the gradient for an ideal Gaussian polymer chain experiencing longitudinal elongational flow under steady-state conditions. The resulting equation, based on a dumbbell model, exhibits an initial average end-to-end separation equal to the unperturbed random coil value; the separation increases monotonically with increasing velocity gradient, in agreement with recent experimental measurements and with a classical treatment based on a diffusion equation. This approach is contrasted with one based on Hooke's law where the end separation remains zero with increasing gradient until a critical value of the gradient is reached at which point the chain suddenly expands to an appreciable fraction of its fully extended length.