Good reply, cadillactaste. It takes time and patients ... you can't rush it.
Where are you trying to pet her?
Where in the cage is she when she squeals?
Certain things are general and other things can be specific.
If you try to pet one on the head ... it is much like a predator coming over her. Birds are a natural predator of chinchillas and always come from above. This is frightening to her.
If you try to pet one on the cheek ... you might be brushing against it's whiskers. The whiskers are ticklish to a chinchilla and chinchillas do not like to be tickled.
When changing from one cage to another, a chin needs time to adjust ... some will even become upset/stressed if you move their cage to a different room or a different part of the same room or at a different level. Chinchillas prefer to be chest level or above. When the cage is waste high or below, tomany things are moving above the chinchilla for it to feel comfortable.
Jo Ann