I get this question all the time: how much do they smell?
It doesn't matter if we're talking about chinchilla, rabbits, guinea pigs, etc... the answer often has to do with... how much / often are you planning on cleaning?
Really, that is the truth. Even for guinea pigs and rabbits, which, I admit, have much wetter, messier cages, much quicker than chinchillas... I know of people who spot clean daily, or even clean out the entire cage every few days, instead of every week.... those pets don't smell so bad, and mostly you smell the bedding in those cases.
Versus, there's some people clean weekly... if that... if they can find time to do so, in their busy schedules. Those pets are going to smell more.
This is just a fact of life. If you put old food in the trash, and you take the trash out daily... it probably won't smell. If you put old food in the trash, and take the trash out a week later... it probably will smell (at least, more than if you took it out right away). Common sense.
I've had people ask for all sorts of tips and tricks for how to keep their cages smelling nice. There's no magic trick to it... it's as simple as... clean often, and it won't smell.