Neutron-proton equilibration was studied in dynamically-deformed nuclei produced in reactions $^{70}$Zn+$^{70}$Zn at 35A MeV. The composition of the two largest daughters of each excited projectile-like fragment is examined as a function of alignment angle. The lighter fragment is initially neutron rich relative to the heavier fragment, and the compositions evolve towards each other exponentially with increasing angle. The alignment angle, as a result of rotation, is related to time through the angular momentum of the projectile-like fragment, and a rate constant of 3 zs$^{-1}$ is extracted. This corresponds to a mean equilibration time of 0.3 zs. This technique provides a new window through which to gain insight into the nuclear equation of state.