Yup a profit or it's a majority of your income. As a hobby farm you are supposed to keep records and claim any income. Doubt they would ever audit a backyard farmer. Unless you are selling a lot of eggs or raising chicks to sell, I think it would be hard to really show a profit taking into account expenses for feed, coop repairs, etc.
Try keeping records for a few months or a year and I think you'll find it's a wash even with a couple dozen birds.
Unfortunately as a hobby farm if you operate at a loss there is no deduction opportunity.
I figure if the extra eggs pay for the feed and bedding, etc. them my eggs are free and it's a cheap hobby.