Bicycle Mechanics - Chain & Rear Derailleur help needed, please

I have a 2000 Specialized Enduro Elite 3 x 9 gearing, LK FD & XTR SGS RD.
With the chain on the largest chain wheel & the 6th largest cog the chain skips over some the tension pulleys teeth.
I've checked and the RD is not bent. The Pulleys are in line with one another as they should be. I do not have a stiff chain link.
When the chain line is more straight the chain rolls smoothly over all of the tension pulleys teeth and does not skip over teeth and then Jump back in line.
I've change chains and the problem has lessened, which makes me think I have a chain issue. The tension pulley spins freely
I would like to fix this issue if possible before installing my new chain.
All help is appreciated.
Thanks in advance,
Uni

What chain did you change to? I'm not 100% clear on what the problem is but if you had a chain that was so worn that it would not run smoothly through the derailler, I'd be looking to replace the cassette as well. another source of the problem could be stiff pivots in the rear derailler.

Derailleur hanger may be twisted in vertical axis so that the pulleys don't rotate in the same fore-aft plane as the chain.

The cassette is like brand new. There was no chain on the bike. I've tried 2 chains. The chain on the bike is in new. I'm changing to a silver chain Only skips when the chain line is beyond the 6th cog & largest chain wheel..

Derailleur hanger may be twisted in vertical axis so that the pulleys don't rotate in the same fore-aft plane as the chain.

Thanks. If this is the case, will I be able t o see the twist or will it be necessary for the LBS to put a derailleur tool on the hanger and measure it, and would this skip only occur in the gear combination (and higher)
that I wrote about? Fortunately the DH is replaceable on this bike.

I took a look at the RD hanger. It is straight inline with the rear dropout.

I took a look at the RD hanger. It is straight inline with the rear dropout.
It doesn't take much misalignment to throw off indexed shifting. Simply eye-balling the alignment isn't sufficient. Take the bike to a shop where they can do this properly.

I took a look at the tension pulley again. I'm going to change it, when it spins the teeth break the plane. Hopefully this is the problem.

I took a look at the RD hanger. It is straight inline with the rear dropout.It can be straight up and down, but it can still be twisted.

Hold a pencil vertically. Keep it vertical and spin it on its axis. Imagine aiming the derailleur pulleys in or out to point towards the chainrings. Heck, I've seen derailleur hangers that were perfectly vertical, but twisted 90-degrees so the teeth of the pulleys were aimed at the spokes! Chain definitely didn't like taking a 90-degree bend to wrap around those pulleys!!!

I took a look at the tension pulley again. ... when it spins the teeth break the plane.
The pulley bearing may be worn out, or the axle may be bent or dislocated somehow in the cage, though I would suspect a twisted cage first. Take the cage apart and inspect the bearings and axles (I recommend taking pictures as re-assembly can be a little confusing).

Thanks everyone changing the tension pulley solved the problem.

Bad pulley bearing, then.