If I can add to Jens post....
The best way to check chain tightness is to get a set of ratchet straps. Remove saddle. Loop them over the rear subframe at the Y junction (you do Not want to stress the rear of the frame!) And fasten onto swingarm. Get some one to sit on the bike to load the suspension till the swing arm is horizontal as Jen says. Tighten the straps to hold the swing arm there. (Do not try to compress the swing arm by leverageing the strap ratchet). Prop the back wheel up and turn it checking to see when the chain is tightest (yes, it does change). When you have found the tight spot make sure the top loop of the chain is tight, the bottom should have about an inch play taken from the middle point of the chain(check your manual) I.e half up and half down. Once you have set this correctly you can loosen all your straps and with the suspension unloaded check how much free play you have. If it's now three inches or whatever, next time you set the chain tightness, set it for three inches slack unladen.
And yes, a overtight chain will grind like hell.