Sounds like the adjuster's as far back as it goes and you need a new chain.... If you've got service receipts, can you work out how many miles are on the chain?
the eccentric adjuster could in the wrong position !! there was a thread about this on the old board but i can't find it it was explained by shazzam as i had a similar problem with mine it was confusing at first but i got it worked out in the end .
but as nick says check your chain isn't shagged first
Basically you want the centre of the axle lower then the centre of the eccentric. When you turn the eccentric you'll see the swingarm rise and fall - you want the swingarm high.
To check your chain for excessive wear measure over 16 links, if it's longer than 256.5mm it's knackered. Also check the teeth on the sprockets, any "hooking" and they can go in the bin as well!
Whatever you don't leave it as long as I did, I assumed 16000 miles would be no problem for a chain and sprockets, for the last few hundred miles I could hear a strange sound from the back of the bike, wasn't til I went to lube the chain that I noticed 5 missing teeth from the rear sprocket!
As NBs says...your hub must be at its maximum for chain tension (at a 3 oclock position if viewed from the sprocket side. If thats the case, rotating it either way will only slacken the chain. If you have recently bought the bike, then I imagine the dealer/previous owner just didn't bother splashing out on a new chain.
New chain needed by the sounds of it, unless the chain is fine, and the previous owner run different gearing, a bigger rear sprocket, and changed it back prior to selling...which may explain why the chain is now slack even when maxed out?
Anyways...new chain about £65 from Nelly/Mike Davies. Can recommend the Tsubaki Heavy duty X ring in gold...look good too!