Final answer:
The Andean rodent with the softest fur in the world is the Chinchilla, option A, valued for its dense and luxurious fur.
Step-by-step explanation:
The small Andean rodent prized for its fur and known to have the softest fur in the world is the Chinchilla. The options presented are all rodents, but among them, the chinchilla is especially valued for its dense and soft fur, which has made it a target for fur farming and has even led to their status of being endangered in the wild. While the capybara, degu, and viscacha are also rodents of South American origin, the luxurious fur of the chinchilla is unmatched, making it the correct answer, A) Chinchilla.