Firstly... I'll have one of whatever Ciro is drinking!
then I'll add some fuel to the fire and say again) ... wouldn't a battery qualify as a chemical reaction!!
us chemists can be everso annoying!
Somehow you have to store energy, but (depending on what the rules say) if you were to use electricity from the national grid (or a power source external to the craft) boiling the water would give some serious thrust - the change in volume from liquid to vapour should be a good way to propel the craft.
hmmm ... and then I think, how about dry ice, that'd give you a means to create a pressure differential, a 'tank' of water, drop in a lump of dry ice and put the lid back on, and of you go...
The possibilities might not be endless, but there are cetainly several solutions.