Look for the following things before buying a chinchilla:

1. Chinchilla should be bright and curious in attitude, and not lethargic. This can be hard to judge in a sleepy chinchilla, but generally chinchillas should wake up and be inquisitive about what is happening when people pay attention to them.  
2. A chinchilla's coat should be well groomed, and very thick, fluffy, and shiny. There should be no clumping or mats and no bare patches. Also check for soiling (faeces or wet fur) around the rear end, as this may indicate a problem with diarrhoea. The skin should be free of scratches or sores.  
3. The eyes, nose and ears should be clean and free from discharge. Check the fur around the eyes and nose for signs of wetness, staining or crusts.   
4. Try to get a look at the teeth, they should not be overgrown and should be well-aligned. It's normal for the teeth to be yellow-orange, especially as chinchillas get older. Also check for wet or matted fur on the chin (overgrown or misaligned teeth can cause drooling).   
5. Observe the chinchilla's breathing, which should be quiet and not laboured, with no wheezing, clicking or gurgling noises.  
6. Watch the chinchillas move around - they should have no signs of lameness, stiffness, or reluctance to move around. Their tails should be held high and they should be quite active -- chinchillas are normally very quick and are able to jump well.   
7. Look at the chinchilla's surroundings. The cage should be clean, with access to fresh food, hay, and water, and not overcrowded. chinchillas kept under good conditions will be less stressed and have less exposure to disease.  
8. Observe how the chinchillas reacts to people -- most will be skittish at first but ideally try to pick a chinchilla that is curious and will approach your hand in the cage, at least for a quick sniff. A chinchilla that hasn't been handled much will probably not want to be held, but try to find one that isn't panicky, or that tries to spray you or rears up and growls at you. Chinchillas that make aggressive moves are just fearful, and most likely can be tamed, but will require more patience before you will be able to handle them.   
9. It's possible to keep more than one chinchilla together, especially if you adopt a young same sex pair (litter mates are a good choice, or chinchillas that have been raised together from a very young age). Try to find out the age of the chinchillas, and adopt chinchillas that is as young as possible (they are usually ready to be adopted by about 3 months old).   
10. If you go to a breeder, you may have a better chance of finding a young chinchilla that is used to handling. You also have a better chance of finding chinchillas bred for temperament and health. All breeders are not equal, though, so ask breeders about how they handle and care for their chinchillas and their breeding goals.   
11. If you go to a pet store, and any of the chinchillas at the store seem ill (even if they are not in the same cage as a chinchilla you want), do not adopt from that store (if an illness is contagious, your chinchilla may be next and there may be possible heartbreak ahead).  
12. Make sure the males and females are separated. Familiarize yourself with the differences between males and females, and if a store doesn't separate them or seems unsure about the gender of the chinchillas, move on. It is best to avoid the possibility of surprise litters, especially in very young chinchillas. They can become sexually mature as early as 4 months (8 months is more common), but getting pregnant this young would be very unhealthy for a chinchilla. 

 T hough you may not be able to handle a potential pet chinchilla, you should be allowed to at least put your hand in the chinchillas cage to try to assess temperament.