Yes chinchillas can eat carrots.
However chinchillas have very sensitive stomachs so don't feed the chinchillas too much carrots or other vegetables.
If you do feed the chinchilla too many carrots or too many other vegetables then the chinchilla can get stomach pain and even diarrhea.
If you're chinchilla has diarrhea and you're feeding them carrots or other vegetables then it's usually a sign that you're feeding too many carrots or too many other vegetables to the chinchilla.
Just feed the chinchilla small amounts of carrots or other vegetables and they will be fine.
Besides carrots chinchillas like to eat raisins and sultanas.