It has been understood for many years that a polymer molecule will uncoil in a coil-to-stretch transition when it is placed in an extensional flow with a strain rate exceeding the slowest molecular relaxation rate. This paper looks at the effort which must be exerted to achieve this uncoiling, in other words the transient stress in a dilute solution of such uncoiling polymer molecules. Numerical simulations have been performed of an isolated linear chain of inextensible links which are freely hinged, the chain being placed in an axisymmetric extension flow. Hydrodynamic interactions between the many beads are not included. During the uncoiling, the stress is found to be mainly dissipative rather than elastic, i.e. the stress is proportional to the instantaneous strain rate rather than being independent of it. A rapid build up of this viscous stress with the total strain is shown to come from the growth of segments of fully stretched chain. The evolution of these segments, the growth in their size along with the reduction of their number, is examined with a simplified 'kinks dynamics' model. The above theological behaviour in transient strong extensional flows is not described by the standard constitutive relations which have been used in the past for dilute polymer solutions, e.g. the Oldroyd-B fluid and FENE dumbbell models. A suitable modification is suggested, which gives large strain-dependent viscous stresses.