I'm an insurance adjuster so maybe I can shed some light on this, bearing in mind that policies differ from company to company and state to state ...
Typically the liability portion of your homeowners insurance (or tenants insurance if you're a renter) does not cover claims arising out of your business or farming activities. That's because you should have a separate commercial policy to cover those activities (your homeowners insurance isn't designed for it). That being said, most insurers will be happy to add a hobby farm endorsement to your policy for a very small fee if you just have a small operation. Others may say that such small-scale egg production doesn't count as a farming activity in the first place and you may already be covered for it.
The best thing to do is talk to your insurance broker where you buy your insurance and they'll either make a note on your file so everyone knows you're covered for your chicken activities, or charge you a small fee for a special endorsement (or, if your current carrier gets the heebie-jeebies over chickens, they can change you to an insurance company that will accomodate you). Either way you can go home and get a good night's sleep.