My 1998 Subaru Legacy makes a chattering noise from the rear differential when I acceletrate hard, there is no noise if I accelerate lightly or at any other time. It is suggested that a differential oil additive may help if so what additive or oil ?

That would probably be in the differential or bad universal joint.

you will likely need to replace the following:
Duty C Solenoid
Transfer Clutch Pack
Reduction gear
All of these parts are located in the tail end of the 4EAT automatic transmissions. The reduction gear can separate from its hub and damage the above mentioned parts too.

Here's a guide for your ABS brakes Harvey. Repair Guides Four Wheel Anti lock Brake System Diagnosis And Testing...

check the gear oil level and condition in the rear differential. if you can rule out wheel bearings then this is what to check

This recently happened to my 98 Subaru Legacy Outback.
My problem is in the rear differential. May be the same for you.
When making a turn, the car sounds like a Star Wars T.I.E. Fighter. The outside wheel is not turning fast enough to keep up with the inside wheel or vice versa. AWD is disengaged and car is currently operating on Front WD. I was told this is fine to drive this way.

I have this same problem with my 1996 Subaru Legacy 2.2 Wagon. There is a Subaru Service Bulletin #16-62-97 dated 5/16/97 with a Subject entitled "Transfer Clutch Binding And/Or Bucking On Turns". There is also an important follow-up to it numbered 16-64-99 dated 09/15/99 entitled "Revised Transfer Clutch Assembly Replacement Procedures" that should also be used should you decide to go ahead with the transfer clutch replacement.

I just got these Service Bulletins from my mechanic who got them from a Subaru dealer.
The estimate was about $700-$1000 to fix. This is more than likely the cause of the binding problem on slow, sharp turns.

Dan Hunt
Danbury, CT

there is a plug on the shaft-side of the differential. Using a ratchet remove the plug and with the engine OFF, stick your finger inside the hole and you should get fluid just below the threads of where the plug goes in.

juddering is UK english for shuddering in US english. The center bearing shouldn't move, i/e/ the shaft should rotate w/o side play in the bearing, but the rubber mounts for the bearing should be flexible. The needle bearings in the universal joints in the front to rear drive shaft can go bad, causing noise when accelerating and they're not changeable w/o special tools. Your problem also sounds like differential, which would mean that you need to change the gear oil in the rear differential. As the oil ages it stops working properly in the limited slip differential even if visually OK. Do the front differential at the same time, engine heat ages it even faster. The center diff is in the AT, so you would change the AT filter and fluid.
How to tell which problem you have... in a parking lot with dry pavement, stop the vehicle, turn the wheel hard right, accelerate a moment, and repeat hard left and centered. If its worse turning, than straight suspect the differential fluids first. If its the same turning or not and especially if its the same on wet or dry pavement and at slow and high speed then look into the propeller shaft first.

One way to track down the noise; since sound travels through metal its hard to pinpoint when driving in the car.
Jack all four wheels off the ground securely (preferably a lift) and run the car with the wheels spinning. Then, without dying, listen for the noise. The dealer can do it for you as well. But sounds like a bad differential.

Sounds like it could be the rear end differential.