Chinchillas are incredibly adorable little fluffballs, similar to a small-eared rabbit but with far denser fur, which almost caused them to go extinct from pelt hunters in South America. Instead of covering what DyRE already noted in his writeup, I'll chip in some additional information from personal experience.
Chinchillas are long lived. Most people don't really understand what that means when they buy the cute fuzzy rodent. The average lifespan is around twenty years. That means they're going to outlast your little kids when they move out or go to college. If you've had a breeding pair, you can expect to have them in your life for a very long time. In fact, the majority of the owners I know are the third or fourth adopters.
The first two chinchillas that hopped into my family were Fatty and Skinny, the former a male and the latter a female. The young woman who had them originally gave them to my oldest daughter with a small cage. Fatty was constantly trying to hump Skinny, so she kept her business end stuck in a corner at all times. They were already twelve years old when we got them.
Chinchillas love to move around, including running and hopping. They can actually hop a surprisingly big distance when they need to, like Skinny trying to escape the letch. Their cage was too small in my Official Dad View, so of course I went out and got a $400 four-level ferret cage. They were nervous at first, but went off exploring as soon as they realized there were no hawks or snakes hiding in there with them.
Chinnies are also one of the smartest rodents in the world -- some say the smartest. They'll find ways around things and can learn how to open simple latches, which was another reason to get a better home for them. They enjoy lots of interesting toys and places to hide, plus they love to find the highest spot to watch over things in the cage. I got our two chinnies an expensive running wheel for exercise but their favorite thing to do was to climb on top of the wheel and balance, surveying their domain.
It is important to keep chinchillas clean. They don't help you much because each one can poop hundreds of tiny turds a day. They are oblivious to the act of pooping, so you'll find the little craplets everywhere. I would highly recommend a cage with a metal lip around the edges of each platform because they scatter their poop seeds everywhere if they decide they MUST GET TO THAT SPOT OVER THERE RIGHT NOW. There are a few folks who do not recommend wood shavings for bedding. I personally prefer either shredded or pelleted recycled paper. They absorb a lot of water and you get karma points for recycling. The rodents do prefer to go to certain areas to pee, expecially corners, so it is easier to clean that stuff. The poop and pee does not smell bad unless you don't clean the cage. With two chinchillas I normally clean their four-level cage every two weeks. Bedding does end up costing more than expected, so factor that in to your adoption plans.
The fur for the chinchillas keep them warm, so it is important to keep them in an environment that does not get too hot or they'll die from heat stroke. The highest I let my house get is 75 degrees, but around 85 you're asking for trouble.
Chinnies drink a lot, and I would recommend a large water bottle with a stainless steel ball spout plus an additional small water bottle on a different level. They'll tend to use one, but the other bottle is just in case you're unavailable and they run out of water or, as happened on several occasions to me, you don't quite thread the spout on right and it empties itself overnight. The paper pellets absorbed two quarts of water, by the by.
Chinchilla food can be stupidly expensive at Wal-Mart or Petco. I go to a feed and grain store and get 50lbs of vitamin-enriched rabbit pellets for $12. Twelve bucks would get you a four-pound plastic bag of the same food in Wal-Mart. They also should have a supply of Timothy hay, as it helps with their digestion and they look cute nibbling while they slurp in a stalk like stiff spaghetti.
You will want to give them snacks. Lots of snacks. Remember how I told you that they're smart? They know how to look adorable and cute, running up to the bars to greet you so you'll give them something tasty. You must resist the urge to do this. Chinnies have sensitive digesting systems, and they can get diabetic if you give them too many sweets. I give mine dried rose hips every two or three weeks (good for vitamin C). For a snack every other day, I give them either a raisin, a tiny chip of dried papaya, or a snack called Vitakraft Drops, made from dandelions specifically for the breed. If you want to give them another snack because they're guilting you with their big eyes, you can give them a small piece of shredded wheat or a Cheerio. They will sit on their haunches and hold the snacks in their tiny dexterous hands and nibble away.
Chinnies love taking dust baths. They do not lick themselves or use water to wash. You must understand that this dust will get everywhere. Every other day is fine. Most folks use an enclosed plastic house that is tinted or clear to watch them go berserk as they spin and flop around. It's hilarious, and the dominant chinchilla will insist on hogging the dust bath first. You may have to boot him so the other chinchillas can get some bath time. Remove the bath house when they've had enough time otherwise one will move in and fill it with poop and pee.
Speaking of fur, besides having one of the densest furs in the world, they have a nifty ability to open their pores and release their fur. It's a survival skill, and it allows them to get away by releasing their hair and running away. Better to look bald and silly than to be digested. If you're picking one up and it gets spooked, don't freak out if you end up with a large handful of fuzz. It doesn't hurt them except for all of the other chinchillas making fun of him when you go to sleep. Oh, yeah, they're mostly nocturnal, but do like waking up to see what you're doing and to goad you into giving them something tasty.
Most folks assume chinchillas make no noises besides the patter of tiny prehensile feet. They do make a lot of weird noises and squeaks. It's not constant, maybe two or three times a day, but the noises are cute unless they're fighting over who will be trying to mount the other one.
Chinchillas need things to chew. I make sure to give them lava ledges to climb and chew, and I give them chew logs and applewood sticks. I also keep a salt and a mineral block next to their hay basket. If they don't chew enough, their teeth will grow and will have to be ground down by a veterinarian. It's important you find an exotic animal vet near you that knows chinchillas. I drive 60 miles to my nearest one if needed, and a teeth grinding runs $40 since they have to put them under anasthesia.
Eventually, your chinchillas will start to pass away. Skinny, the female, died in the bathhouse when she was 16 years old. Chinnies are communal, and we were concerned about Fatty. I didn't want to go to the store any buy another 20-year project that will literally outlast me, so we searched around and found a chinchilla rescue. We adopted another older chinchilla because nobody wanted one that will die in five years. This one was a male, and we had already had Fatty fixed to allow Skinny to have a few years of peace. We renamed them Jay (the new one) and Silent Bob (Fatty was kind of sad without Skinny around). These rodents are competative, and they tend not to show any weaknesses or problems until they fall over. Jay was the most active and fun little chinchilla until I was petting them and he fell over. He was twenty, and I held him as he passed away. I still have Silent Bob, but since he's at his max age I don't want to get another chinnie. I spend a lot of time talking to him.
Are they worth having around? Yes, I do think they are. They're not the types that will jump on you when you get home from work, but if you get a small pet fence you can sit with them and play. They're friendly and if they nip they pinch, rarely breaking the skin. Don't, by the way, use the plastic balls that allow them to roam around. Some adoption places will deny your application if you are going to do that. It's apparently bad for them. They'll learn your voice and will do silly things to get your attention. Make sure you give it to them often.