We report a direct measurement of the friction coefficient of a fluctuating (and slipping) contact line using a thin vertical glass fiber of diameter d with one end glued onto a cantilever beam and the other end touching a liquid-air interface. By measuring the broadening of the resonant peak of the cantilever system with varying liquid viscosity η, we find the friction coefficient of the contact line has a universal form, ξ(c)≃0.8πdη, independent of the liquid-solid contact angle. The obtained scaling law is further supported by the numerical simulation based on the phase field model under the generalized Navier boundary conditions.