Guess I'll be the one to go against the grain.
It is correct that chinchillas don't NEED vegetables in their diet. In the wild they are not "garden groomers" like rabbits are. Hay and pellets are quite adequate.
That being said, from a nutritional/veterinary standpoint, dark leafy greens can be a nice healthy treat for them. TREAT means it should not make up more than 5-10% of their diet. Think about how much they eat in pellets and hay, and that equals a very small amount of greens. As with any treat they should be introduced gradually into the diet.
I've tried greens with a couple of chins that were not eating, in an effort to get them to eat SOMETHING. One nibbled on them, and one completely turned her nose up on them. Some good greens are romaine, green-leaf and red-leaf lettuce. No iceberg lettuce.