I give mine the raw/natural oats (the long thin kind) and/or the cracked natural oats, they love it. I treat it as a supplement mixed with a couple other things ... they only get 1/2 teaspoon daily and absolutely love it!
They also get the original Quaker oats (the kind you have to cook, not the instant), but I only give the original Quaker oats once or twice a week and about 1/4 teaspoon, hand fed. I treat it like a treat, they want more, but I don't like to mess up the balance of their diet. They would eat the Quaker oats and leave their pellets (which are best for them), if I let them have the Quaker oats very often.
Chinchillas can live on hay and/or hay and pellets alone, (and fresh water) if the pellets are of good quality. The 'treats' or extra things we give them have to be limited, or they will want the extras and leave what is the best for them.
Jo Ann