Cheetahs eat gazelles, zebras, and antelopes. As a matter of fact cheetahs don't have many predators. Most animals go after cheetah cubs. Cheetahs could easily outrun their predators. Cheetahs like to stalk their pray.
The food chain is kind of complicated. As you can see this is a food chain of the Savannah. Hyenas are the top predator. They are the one's that eat cheetahs. Cheetahs are pretty much at the top of the food chain. Lions also eat cheetahs. Cheetahs have a pretty good chance of surviving.