No, a chinchilla can’t actually eat rope but they can chew on it if it is in their cages.
As a chins teeth constantly grow throughout their life it is important that they have things to chew on in their cage at all times.
One of those options is rope. A chinchilla wouldn’t normally actually eat pieces of the rope if there is other food items available in their cage.
However it should be safe for a chinchilla to nibble and chew on rope in order to grind down their teeth.