Droplet pinch off, which occurs when a drop of liquid detaches from a capillary, can be strongly modified in the presence of polymers, giving rise to long and slender filaments that thin slowly in time. However, little is known experimentally about the molecular conformations of the polymers in the filament itself. Since the thinning dynamics of these filaments can be used to extract macroscopic quantities of interest such as the elongational viscosity of polymer solutions, which is of importance in a variety of physical processes (electrospinning, spraying, or drag reduction), the link with the molecular scale dynamics would be an important step towards understanding the extensional properties of such solutions. We show here, experimentally, that the polymers are highly extended within this filament region and that the distribution of these extensions is stationary in time. We then determine the elongational viscosity from the full filament dynamics. Such a determination turns out to be consistent with the polymer extensions observed and also consistent with simple models of polymer elongational viscosities. The direct observation of stretched macromolecules within such suspended liquid filaments suggests that these filaments may be useful for preparing polymeric materials with specific anisotropy or for optical screening of biopolymers such as DNA.