When the chain is on the large chainring at the front the chain and derailleur are under higher tension. The chain line is also subtly different. This said, the chain should run smoothly regardless of which chainring it is on. Have you tried adjusting the barrel adjuster on the rear derailleur just a quarter turn or so to see if you can dial it out?
Is it definitely making noise at the rear or is there a slight rub coming from the front derailleur on the chain?
Rear derailleur hangers can go out of alignment quite easily also, it only takes a very minor shift to have a significant effect.