We report on the phase noise measurement of a millimeter-wave synthesis chain developed for a continuous wave (CW) source exhibiting high frequency stability. We quantify the performance of each multiplication stage in terms of phase spectral purity. From the initial cryogenic sapphire oscillator generating 12.97 GHz, a total multiplication factor of eight is applied through two stages to reach a frequency of 103.75 GHz. We find that the chain performance is primarily limited by the phase noise of the initial frequency doubler.