What kind of farm animal can I have in my backyard without my neighbors noticing.

Chickens may be an obvious answer, but even hens make enough noise to be noticed by a neighbor. If it's eggs you want, then choose quail. Quail are small and require less square footage than other birds, they are quieter than chickens or ducks and a hen can lay up to 300 eggs a year. The trade off is that the eggs are smaller and you may need to adjust recipes, three quail eggs are the equivalent to one chicken egg.