If the cat clone survives then rich pet owners whose animals die could have them born again in a lab.
A very rich American man called John Sperling is paying for the experiments, and if they work he hopes to set up a company to clone pets for wealthy people.
Useful to society
Sperling has also said that he would like to see the cloning extended to animals that are useful to society, like rescue dogs.
Most cloning so far has focused on making animals that can help people, like improving the milk that comes from cows, or making it possible to use animal organs in human transplants.