My first question is, how do you know she's lonely? Is she off her feed? Losing weight? Not playing when you take her out of the cage?
My second comment is that there is absolutely no way to guarantee that she will tolerate a cage mate. You can definitely try to introduce her, but make sure that you are prepared to have a separate cage for the new arrival in case they don't get along. Also realize that whether they get along or not, you made a commitment by bringing that chin home. You made that choice, the chin didn't. If they don't get along, I would be sad to see an add in the classifieds "chin for sale, doesn't get along with my chin." You will be warned by everyone on this forum that that is a very real possibility. So if you are prepared to have two cages, are able to afford vet care for another animal, etc., then give it a try. Also know that even if they do get along, you will still have to keep that cage on hand because there are chins who can get along for years and then they suddenly turn on each other. More than one chin equals more than one cage on hand.