The hybrid will be fertile, there is lots of evedence there is a small amount of grey jungle DNA in all domestic chickens, in fact where humans live near wild grey jungle fowl populations they are going extinct as a pure species because in the wild a male grey jungle fowl will only mate with a pure grey hen but a hybrid and a domestic chicken will mate with a hybrid or a pure hen, leaving less and less pure hens every year so the species is disappearing from areas where the humans cohabitation. In captivity a male will accept a substitute, but in captivity animals often exhibit unusual behavior not seen in the wild.
It is future generations that do not have crosses of pure blood, for instance breeding just hybrid back to hybrid that the chicks become unable to continue as a viable line.
By the way, mules can be fertile, though rare, recent studies put the number up to close to about 10% in females and no one knows in males because they are castrated at birth because an uncastrated jack is very aggressive so they are never left intact.
