Your 500 has a double-row chain. The only V-8s afflicted with the single row chain were the '81-'83 US 380s. They reverted to a double-row for 1984. Be careful about the brand of chain you use; MB or IWIS seem fine, but one of the other brands (which I can't recall) seems to have caused at least one report of premature stress cracking. Given its importance, a replacement chain is not all that expensive, so get a good one.
You might as well change the oil while you're at it. Don't worry about breaking in the old stuff (still chuckling over that one). The rough idle could be a number of things: a faulty O2 Sensor is a possibility (although if the engine idles unevenly when cold, it probably isn't the O2 sensor), but it could also be an ignition system problem (even using platinum or incorrectly gapped spark plugs has been known to cause idle problems), warm up regulator, idle speed controller, etc. etc. etc. Many of these components are rather expensive, so you should try to arrive at a reliable diagnosis before you begin replacing parts.