Pekin ducks will do that for you.
In chickens, what you are asking for is a contradiction in terms. Ether they grow slow and are good egg producers and reproduce themselves, or they are a fast growing hybrid, which by definition means they don't replicate themselves.
Some people try keeping hens from their Freedom Rangers or Cornish Cross and breed them to heritage breeds. I don't know that anyone has had monstrous great success at it.
One of the universities has just released a new breed that does close to what you want. They are developed for 3rd world countries and as far as I know are not being released inside the USA. I'll have to look up the name of the breed and the university. Don't know it right off the top of my head.
