I have had trios in the past and am going to be trying again to introduce a chinchilla to an already bonded pair. I use the following methods and have always worked for me...I start my placing cages side by side for at least a week or longer. I gradually move the cages closer together every few days...if I see they start acting territorial, I dont go any closer until they have calmed down and dont seem as bothered. Once they are about 2 inches apart and not making a fuss, I will let them out for play time together for 5-10 minutes and if that goes OK, I let them have this play time each day for a week but each day gradually increase the time. If no problems, then I leave their cage doors open and let them wander in and out of each others cages...if that is fine, then I put them in the cage I want them all to be in, and close the door...if at any time there is any fighting, I go back a step until there is no fighting. Some chasing is fine, and mounting as well, but anything more than that, I separate right away and go back to the first step.
Now, with that being said...it also depends on what sex chinchillas you have...I am assuming that all three are girls since they came from a rescue and you are not breeding...this method should be OK. But, if you were introducing a female to a a male/female pair, I would actually approach it differently. I would remove the male and try to bond the females first, then once they are caged together, introduce the male back into the cage. I have had some that are easily paired and others not so easy. In the end, they all have different personalities...I think going slow, a chin would rather be with another vs being alone, but some are used to being alone and dont want a cage mate...I have yet to see that myself, but I have heard others say that is their experience. Hope that helps.