Yes, welcome to reality backyard! Life is impossible without death. Only photosynthetic plants are able to produce their own food; every other living thing has to live off other living (or already dead) things. Many of the animals you were enjoying before the foxes came along - including the birds, raccoons, opossums, and even the squirrels - have been eating one another and other animals all along. Predation is everywhere; we just don't see it all that often.
Foxes - like raccoons and opossums - are opportunistic omnivores. They do eat many small rodents, including chipmunks, as well as bird eggs and young when they find them. For more-complete information on fox diets, please see the links below.