The chance (random) coincidence correction factor (CCCF) for the counting geometry of a Cs-137 point source placed very close to the end cap of a high-purity Ge coaxial detector with 50% relative efficiency was evaluated by a time-dependent Monte Carlo approach. The probability distributions of gamma-ray and X-ray energy depositions in the detector crystal were obtained by use of the MCNPX code. The signal resolving time of the electronic parts, one of the parameters needed for time-dependent Monte Carlo simulation, was evaluated experimentally by the moving-source method. Another parameter also needed for the simulation is the signal pile-up rejection time interval. A random pulse generator was replaced with the detector for this purpose and the value was calculated iteratively by comparing the spectrum obtained experimentally with the spectrum obtained from the time-dependent Monte Carlo simulation of the random pulse generator. A pulse train with a Poisson distribution in time was created, and these parameters with energy deposition probability distributions were used for theoretical determination of the high-count-rate spectrum and the low-count-rate spectrum. The CCCF for the experiment was calculated as 0.92 by our comparing these two theoretical spectra and agrees well with the experimental result, 0.94.