The interferometric gravitational-wave detector Laser Interferometer Space Antenna (LISA) needs to transfer clock information among its three spacecraft in the form of phase-modulation sidebands. For this reason phase noise introduced by the optical chain between the carrier and a sideband must be low. We have measured this differential phase noise for a ytterbium-doped fiber amplifier emitting up to 2 W. For 1 W of output power as required for LISA, the measured differential phase noise was within its requirement. For 2 W output power the amplifier exhibited stimulated Brillouin scattering and showed a differential phase-noise factor of up to 15 higher. Dependencies on operating parameters and optical length noise of the amplifier were also measured.