Are we to assume the metal chain is holding us to the middle of the room and we only currently have 5ft range of movement?

Grab the bananas and key out of the chest. Unlock the door, lure the monkeys into the room with the bananas, lock the door while they're eating said bananas. You are now out of the room and away from the monkeys. Now you have time to worry about that pesky little chain attached to your leg.

I know it says you need to leave as fast as possible, but under the circumstances of trapping said monkeys, you should be fine with pulling the weight for a bit once you leave the room.

Okay, I will unlock the chest and get the banana bunch, and the hummer.

Since I was young I'm angry for some monkeys, because they are too annoying hahaha.

I will throw all the banana from them and run to the door and locked it. 

and Run as fast I can and remove the chain afterwards by using the hammer if possible.

And if there's a monkey on my way they will taste the wrath of my childhood by the power of the hammer of THOR! Hahahaha!

So lot's of funny answers here, it was never stated the door or chest was locked. The only thing that was locked was the chain but it was never stated it was attached to anything. So the optimum method involved luring the monkeys and making it easier for you to run. 

Either taping the chain to you, smashing most of it off with the hammer, rolling out in a wheelchair (maybe your on a hill) or putting it in a backpack can help you run/escape. As for luring bananas will do but alcobananas, as suggested by @unsaymono, might work even better if these monkeys happen to be drinkers. The best way to distract the monkeys is to use the key to lock the door with the monkey in there though. I never thought of moving the chest myself but that's a great way to move items. Also it was possible to remove something and use it, then return it to the chest e.g. the hammer to smash the chain then put it back in, allowing to to take anther thing out.

Every answer was smart or funny or both so I will give the prize to @everyone! As in everyone gets the winner prize, thanks for playing it was fun to see how everyone solved it.

I would key the door open and hammer the chain or floor near the chain. Unless the chain is not attached to anything on the other end, then roll that out on the wheelchair. I would probably actually drink the whiskey, eat the bananas, and die in the round room though. What kind of whiskey was it again?

Take the key and tape, tape the chain onto you so it doesn't get stuck while you run, open the door with the key and push the chest with the bananas outside to hopefully distract the monkeys and run.

Your wording gives room to outside the box thinking. This is fun, so here goes...

Walk towards the chest and open it. Assuming here that it's not locked, since you didn't say so. Take out the wheelchair and set it up, then put the chest in it. Most wheelchairs are foldable, so that should work. Now, with the wheelchair out, we have room to maneuver inside the chest.

Use the saw to cut the bandage and tape it together to a nice square. Attach that to one side of the broom. I think we're out of tape now. Use the hammer to affix the broom vertical inside the chest. Look here, we've got a fancy flag! I'm wondering how Sheldon Cooper would appreciate this one. Take out the backpack and put the metal chain in it, well, most of it. This works, since it doesn't say anywhere where the other end is attached to. Put it on.

Empty the bottle of whiskey onto the bananas. No, this is not a pity. We need top concentration to stay alive remember? Don't take out the key, since we're only allowed to take out two items (which are wheelchair and backpack). The door isn't locked you see. What did you expect from a monkey mob? Seriously, they are waiting for me to get out so they can lynch me. If the door does turn out to be locked, then the author made a boo-boo. ;-P

Now take a deep breath and focus. Open the door and roll the wheelchair to one side whilst yelling "Free alcobananas!" Then make a run for it. Obviously towards the opposite side as where the wheelchair is off to. Oh, and good luck!

Let's get to the chest and get the key and the banana bunch:
give the bananas to the monkeys and hope that the key will work both for chain and door. Then escape and close the door, because of the monkeys :).

Alternatively you could let the banana bunch stay in the chest and catch some monkeys with it and maybe crush them and eat their flesh… a little evil… . There might be no way besides losing your feet to get away from there and there is no guarantee to be free because of the door anyways…