Long-term stable, sub-femtosecond timing distribution over a 1.2-km polarization-maintaining (PM) fiber-optic link using balanced optical cross-correlators for link stabilization is demonstrated. Novel dispersion-compensating PM fiber was developed to construct a dispersion-slope-compensated PM link, which eliminated slow timing drifts and jumps previously induced by polarization mode dispersion in standard single-mode fiber. Numerical simulations of nonlinear pulse propagation in the fiber link confirmed potential sub-100-as timing stability for pulse energies below 70 pJ. Link operation for 16 days showed ~0.6 fs RMS timing drift and during a 3-day interval only ~0.13 fs drift, which corresponds to a stability level of 10(-21).