We report a direct measurement of the friction coefficient ξ(c) of two fluctuating contact lines formed on a fiber surface when a long glass fiber intersects the two water-air interfaces of a thin soap film. The glass fiber of diameter d in the range of 0.4-4 μm and length 100-300 μm is glued onto the front end of a rectangular cantilever used for atomic force microscopy. As a sensitive mechanical resonator, the hanging fiber probe can accurately measure a minute change of its viscous damping caused by the soap film. By measuring the broadening of the resonant peak of the hanging fiber probe with varying viscosity η of the soap film and different surface treatments of the glass fiber, we confirm that the contact line dissipation obeys a universal scaling law, ξ(c)=απdη, where the coefficient α=1.1±0.3 is insensitive to the change of liquid-solid contact angle. The experimental result is in good agreement with the numerical result based on the phase field model under the generalized Navier boundary conditions.