It may not be impossible in the long term, but would probably be difficult to achieve. That said I don't think anyone has really tried very hard to select for a giant chicken - presumably because there is a big market for "normal sized ones" and so there's little economic imperative. I think the largest chicken breeds come in around 5KG with occasional reports of c 10 KG birds.
Assuming it can't easily be done the short-term limitation is probably the absence of genes predisposing to gigantism in the populations people are working on. That said if a mutation arose that conferred much larger size, then provided birds carrying it can be readily identified, artificial selection could be used to fix it in a population (provided it didn't have deleterious effects that were too severe suh that natural selection counteracts the artificial). Worth noting that, for instance, dog breeders have managed to achieve something like a 100 fold difference in weight between smallest and largest breeds, so I would never say a 20KG chicken is impossible (just difficult!)