I was riding around the neighborhood on my System-Six (1st Gen. Rival) and I'm having this weird chain skipping. It happens when I'm NOT shifting.

I'll be pedaling along and all of the sudden it feels like I'm on the lowest possible gear and my feet start over-spinning for about half a second and then it resumes normally.

I'm guessing it's cross chaining (I was running the smallest chainring with the smallest cog). Does my FD need to be adjusted a tad? Or is it the rear one?

your RD needs adjustments or you cog has worn out..

Could be any number of things.

Since it happens when crossed small/small it's possible that the chain is climbing up and riding the tops of the chainring teeth, while leaning on the inner face of the outer ring. This can happen if the outer ring has pick-up pins and the chain brushes against it as it comes from the outer most sprocket. Shift to that combination and checking that the chain doesn't touch the outer ring. There is no real fix except not to ride in this combination, which is undesirable anyway because it increases wear.

Given that you imply that this is the only combination it happens in I suspect that's the cause, but here are a few other possibilities.

Poor trim or outer limit adjustment on the RD letting the chain climb up onto the smallest sprocket as if to shift then settling in.

A stiff link or section of chain not engaging smoothly on the rear sprocket. Check by back pedaling while pushing the lower pulley forward to slacken the lower chain loop. Watch for any links that don't straighten immediately as they come off the pulley.

A work chain or chainring, though it would probably only skip under load, and wouldn't be one combination only. But it can't hurt to check your chain for stretch (wear). If it's stretched over 1% (1/8" over 12") this could be why it's skipping. Your due for a new chain for sure, likely a new cassette, inner chainring.

Well, the bike is practically in mint condition so I doubt chain wear or RD breakage is the problem.

Since it's 1st Gen. Rival (silver) it has to be the trim right? The new Rival has the trim feature that only Force/Red had previously.

Yes, it could be trim, which in high gear is actually determined by the limit screw. Adjusting the cable lenght would change trim in all the other gears, but in high the cable is slack and the RD rests on the limit. But if it's an RD issue that would argue that it would skip on this sprocket with both chainrings, not just the inner.