1 possible solution:
Do you happen to have some duct tap or rope? The principle are the same for both type of material or any wrapping type of materials.
1. Rap the handle completely once or twice (this will give friction to where the chain make contact to the container).
2. Balance the water container on your chain
3. Make a marking where the chain should be
4. Remove the water container from your chain
5. Wrap both sides of the handle about 10 times **(leaving a gap where the mark indicating where the chain should be)**
Gatewayto seems to have great idea for your situation. Though, I would like to suggest, if your situation allows, using an automatic watering system. I'm currently building my coop and I plan to build a system from 4" pvc and water nipples. Search chicken waterer and you'll se different ideas. I plan on using a similar system for feeding. The ones I plan on using are both gravity fed options which will allow me to not need to refill for a few days or connect a light pressure supply from a hose.