The whole problem is based on an artificial construct that assumes that the state of being a chicken is something akin to being a country with defined borders. Step one cm. to the left and you have crossed into the country. Step a cm. to the right and you have crossed the border and you are no longer in the country.
The evolution of a species does not mean the sudden appearance of a species. One species does not and cannot turn into another species over one generation.
Every offspring is mainly similar to its parents, with probably a few minor changes. I am 2 inches taller than my father, for example.
The whole concept of “missing links” is also based on total misunderstanding of evolution. Every animal, and every human being, (if they reproduce) is a link between their parents and their offspring. Unless your bones or mine are fossilized (VERY unlikely) we are all missing links in our evolutionary chain.
The only way you could have iron-clad proof of the evolution of a species would be to have the pickled bodies of every member of a particular parent-offspring line preserved over, say, a million years, and having dissected the millions of specimens, run DNA tests on each one to make sure you have parents and offspring, and then measure every change between one generation and the next. (This one had a liver 10% bigger than his parent but this was not passed on to the offspring, who had the same size liver as its grandparent. But its claws were longer and this trait became predominant over the next 50,000 individuals we examined, so that 30,000 years later this species seems to have had longer claws on a regular basis, and this had become an established trait.)
Since it is completely impossible to have this sort of record, scientists use the fossil record, knowing that it will always contain huge gaps and must be based on intelligent guesses.