Well the short answer is, it depends what you are trying to achieve.
If you are content to breed a few chinchillas and show them for a bit of fun then pair breeding is fine.
But if you want to do the best you possibly can at the shows then there is no contest, it has to be polygamous.
So what's the difference between pair breeding and polygamous breeding?
Pair breeding is fairly obvious it is the pairing of one male and one female and keeping them together, pretty much permanently.
Polygamous is slightly more complicated it is the mating of one male to more than one female.
Although in theory that can be as many females as you like it is usually limited by practical considerations.
Dave Knight once told me that he had purchased a very expensive male and was determined to get his moneys worth so mated it to twelve females!
I think probably Fred Duggins was more practical saying if you mated a male to more than 5 or 6 females they were more likely to miss mating a female that had come in season.
If you are a pet breeder and want to produce chinchillas in quantity, polygamous is the way to go, you can select for health and production instead of show quality if required.
So how is polygamous breeding done, We use special polygamous cages, that are joined together in a line, they have an inbuilt tunnel along which the male can run and gain access to each female through a pophole, the females are restricted to their individual cages by a polygamous collar worn on the neck.
You have probably heard or should have done that the way to do well at shows is to purchase a high quality standard male, this should be the best possible male that you can persuade somebody to sell you, important qualities are, good size and conformation, good clarity of colour, strong dense fur, so listen to the judges comments before you buy, don,t take the sellers word for it, the judge is independant and does not know who the animals belong to.
The big advantage with polygamous for show breeding is you can mate your very expensive, high quality male to a number of females, I,d suggest at least 3 good quality standard females and then 3 mutations if you want to produce different colours, this gives you three possible chances of producing something outstanding as against one chance for pair breeding. and also the possibility of producing a few good mutations as well. You can take your offspring from your three standard females along to the shows to find out which of your females is producing the best quality.
And the next step? If you just want to keep the one polygamous line going you can work out from the judges comments which qualities you most need to improve and try to find another female that compensates for the qualities lacking, you can replace your worst performing female with the new one.
If you are looking to start another polygamous line you will need another standard male, if you have not managed to breed one good enough, and that means 1st ribbon standard as an absolute minimum, you will need to purchase one, again try to find a male that compensates for any qualities lacking in the offspring produced from the first male, you can then mate the very best females you have produced to this new male and so on.