Some breeders even go so far as to stop the female eating any afterbirths that are produced and removing them from the cage - the arguments for this are that it is not natural for the chinchilla to eat meat based foods and is only doing it as a defence mechanism to hide traces of the birth.  

Other people claim that the female needs to eat the afterbirth in order to reprocess the nutrients that otherwise would be wasted and lost. 

Those breeders that do remove the hay generally suggest that it is best to do so for 5-7 days. 

personally I do not stop feeding hay or other forms of roughage in this time after the birth, my personal belief is that the added fibre is more likely to assist in he digesting and removal of the substances that do build up in the gut and intestinal tract following the birth and eating of the afterbirths.

As an added assistance to the mum following the birth, feed 2-3 raisins.  These have a laxative effect as well as providing short intense energy releases for her to help her recovery following the strain that it puts on her body.

To date I have not heard of an experience where someone has lost a female through leaving hay in the cage, but felt I would add this page to the site in case you come across it and may wonder why it is done.  It also allows you  to make up your own mind which way seems safest for you.