We present a technique for the stable transfer of an optical frequency reference over a kilometer-scale optical fiber link. This technique implements phase measurements and laser feedback to cancel out the phase fluctuations that are introduced to an optical frequency standard as it passes through the fiber. We also present results for a bench top experiment, developed for the Advanced LIGO lock acquisition system, where this technique is implemented to phase-lock two Nd:YAG lasers, through a 4.6 km optical fiber. The resulting differential optical frequency noise reaches a level as low as 0.5 mHz/ radical Hz for Fourier frequencies between 5 Hz and 20 Hz, which is equal to a fractional frequency stability of 1.7 x 10(-18)/ radical Hz.