Since she is new to you, it will be hard to find some of the very early signs of labor. Most expectant moms will consume more water than usual in the 24 to 48 hours preceding birth. Laying on the side is not necessarily a sign of labor (allot of my male chins lay that way), but flattening out on their tummies and having rapid breathing can be one. If you watch closely you can see the contractions. Stretching and even appearing to try to move something by pushing on it are signs of labor. Her cage can look like the neighborhood exercise room at times.
But, as chinclub says, you are new to her and she to you. Labor and delivery can be a stressful time for some chins and privacy is often the most welcome to the soon-to-be mom. Now, if she is not in labor now, and is a month from now, your presence could be reassuring ... as long as you can remain calm and relaxed. Animals sense this. If you are stressed and upset, she will probably be also. Not a good thing for a new chin-mom.
Now, once her water breaks and she starts delivering, she will probably spend extra time cleaning herself. Chinchillas are very clean animals. And lots of time cleaning the kits. The kits will usually "pop" out rather easily, but there is always the possibility of problems. If a kit seems to be partially out, but not come on out with in the next few pushes/contractions. You might want to let your vet know what is going on. If you see blood continuing to flow, call your vet. There is always a chance something can go wrong, but keep in mind millions of chinchillas have been born without the intervention of mankind. It is a very natural thing occurring. Keeping in mind this is true, it is still a miracle each time it happens. Each and every time, I find myself in awe of the miracle of a new life. Especially a chinchilla kit ... they are born fully furred, with eyes open and are usually up and playing within an hour or so. They can even climb the cage wires within the first 24 to 48 hours. For this reason, they need a cage that has wires no more than 1 inch long and 1/2 inch wide. (Kits have been known to crawl/fall through a hole as small as 1 inch square, to the floor and usually to their death.) Cages that are more than 15 inches high will often be the death of a new kit. Kits have the ability and know how to crawl up, but not down. Once they reach the top, they turn loose and fall to the bottom. If they are lucky and do not hit anything (like a hut or feeding bowl) on their way down and have a nice thick layer of bedding to land on, they may have a chance, but not always.
Do you have a second cage for the male? He must be separated from mom and kits for the first 10 days or he will probably breed her again during this time. If she is nursing one litter while her body is trying to develop a new litter at the same time, the results are at best ... bad for all concerned. This is to much of a strain on momma Chin's natural resources and she is not able to produce enough milk for her nursing kits, nor enough calcium to properly form the kits in the next litter. There is allot of responsibility that goes with breeding chinchillas. It can be wonderful one time and heart breaking the next. Being prepaired can often make that difference. Not just being prepared for the emergencies, but also being prepared for the unknown sides of nature, it can often times seem very harsh.
Stay calm cool and collected ... that is the best for you and for your chins. Have a reputable vet that is very familiar with chinchillas and have all the things that your chins need along with proper housing for them and all should end well.
Hope this helps!
Jo Ann