There are many ways to try to get them to get along again, you can get a small tiny cage, one where only one chin will fit into (like a carrying case, but not plastic) and put it into the bigger cage (after cutting whiskers of the dominate chin) and put the smaller cage inside the bigger cage and let it stay there all day, then switch chins after a day. You can put a bit of either vanilla extract or vicks vapor rub on the nose. If you do this put a hideout in the smaller cage, and I would put the more dominate one (the one that starts) in there so that when he gets tired of arguing he can hide out.
Then there is a method called smooshing that some people love and some people hate. But again you would need to buy a small cage so that they can't move around, put the stuff on their noses and they will argue and try to fight, but if the cage is small enough they can't actually fight.
Here's one thing I found on the internet about smooshing, but this is the first time i read it this way but maybe it will help:
One method if introduction is the "Smoosh" method. Basically, take two smaller cages that are just big enough to house each chinchilla and put them side by side in a larger cage. This allows them to get used to each other's scent without giving them enough room to fight, should they feel the need to. It's best to use the Smoosh method during the day, when the chins will be less active.
If that doesn't work, or you don't have the means to try that method, having two cages side by side for a while may be your best option. After a few days, try switching cages so that Chin 1 goes into Chin 2's cage and vice versa. Again, this allows them to get used to each other's scent and usually prevents injuries from possible fighting.