I searched this sub-forum and found the thread
DataIO Error System Error: City. It is an old thread, dating back to '04, but seems to match your problem.
While that thread discusses what causes the problem in-game (which as a programmer I thought was an interesting problem), the solution is to get your version of Civ patched to 1.29 (the patch page is
here) or spend about $20 (less at Amazon) and purchase Civ III Complete.
If you have the cash, get Civ III Complete. I'm cheap, but it is worth it.
If cash is a problem, and at times it is, download and install the proper patch and that will fix your problem also. Your version is 1.07, which is in the bottom left hand corner of the screen.
Civilization III has three versions; the original release, referred to as Vanilla, which is what you have, Play The World (added more AI and Medival Infantry) and Conquests (added even more AI, more Wonders and other things). All three have patches to fix various problems, such as the one you have. In Civ III Complete, all three versions are fully patched and all three install at one time. The installation will default to Conquests but the other two versions have their own folder and can be played apart from Conquests.
If you are not sure of which version you have, start a new game and see what choices of Civs you have. If you can be the Maya, you have Conqeusts. If you can be the Arabs, you have Play the World. Otherwise, you have Vanilla.