A fiber optic system was developed for the purpose of distributing precision timing reference signals to telescope subsystems that are physically separated by as much as 3 kilometers, while preserving the spectral purity and phase stability of a hydrogen maser source and while avoiding cycle ambiguities. The signals are transmitted via single-mode optical fiber to five locations on the site, each 1 to 3 kilometers away, where they are used as references for receiver local oscillators and other signal processing electronics; this imposes stringent requirements on phase stability. Phase jitter (defined here as the total phase noise integrated over offset frequencies above 1 Hz), was minimized by the careful selection of components and by standard phase- locked-loop techniques. Phase drift (phase noise at offsets of less than 1 Hz) is caused primarily by variation of the fiber's electrical length, and is accounted for by re- transmission from remote to master and accurate monitoring the round-trip delay. The system is capable of measuring path length changes as small as 0.1 picosecond. These measurements are not used for real-time correction, but instead they are applied during post processing of the astronomical data. This approach allows coherent interferometry at millimeter wavelengths. Two frequencies, 10 MHz and 500 MHz, are transmitted over one fiber, with their sum providing direct intensity modulation of a diode laser. The 10 MHz signal extends the cycle ambiguity to 100 nsec. A sample of the received 500 MHz is sent back on a separate fiber to the transmitting station where it is phase compared with the outgoing signal. A third signal at 1 Hz is transmitted separately, extending the ambiguity to 1 sec. The fiber length should be extendible to at least 10 km while achieving the same performance, although we have not tested this. Larger distances should be possible with lower-noise lasers. Lower timing noise could be achieved by increasing the reference frequency from 500 MHz to several GHz.