Yes, chinchillas can safely eat grass.
Make sure that you only feed your chinchilla fresh grass to eat though.
They like natural grasses that do not contain any toxic elements that may be added to grass to make it grow more like fertilizer.
Those types of things can cause major health issues for your chinchilla so make sure no pesticides, toxins, or anything have been added to the grass that you plan on feeding to your chinchilla.
Grass helps them with a proper digestive system.
It is actually important to feed grass to a chin as part of their regular diet as it will help promote a healthy life.