Domesticated animals require a continuous breeding effort to keep their desirable traits. This is provided by humans, who select the best specimens for producing the next generation. If the selection pressure exerted by humans is removed for several generations, the animals will lose their domesticated traits and revert to wild forms. This can happen quite fast, because domesticated traits are often unsuitable for survival in the wild, so animals that lose their domesticated traits leave behind more progeny. For example, loss of aggression is nice for a pet or domestic animal, not so great in the wild.

This is what happened to chickens in medieval Europe. Chickens were originally domesticated about 8,000 years ago in India, from red jungle peafowl. By about 5,000 years ago, most of the desirable traits were in place, and they were bred in large numbers for meat and eggs in the Indus Valley Civilization. From there, they spread to ancient Mesopotamia and then to Egypt. In Greek and Roman times, chicken were a big part of the diet. The Romans, in particular, loved chicken.

But after the fall of Rome, there was a precipitous decline. Chicken bones found at archaeological sites from medieval Europe show that chicken shrunk to half their size compared to Roman times. This is closer to the size of red jungle peafowl, their wild ancestors. In short, the domesticated features were lost, because no one was actively breeding them anymore.

Why this happened, we don't exactly know. The Romans had huge chicken farms where chickens were produced on very large scales. It's possible that these huge farms disappeared after the fall of Rome, and not enough people took up the slack in breeding them on a smaller scale.

As a result, chickens lost their popularity in Europe because the chickens they had weren't such a great deal. They were half-wild birds that were easy prey to predators, didn't lay many eggs, didn't produce much meat. They are not native to Europe, and without human protection, they don't survive European winters or European predators very well. Other local animals took over the role that chickens once served. If you look at paintings from the era, you'll see a lot of paintings of kitchens and larders and feasts with swan and geese and pigeons, but not many chickens. These hardier European native birds handle the lack of human protection a lot better than chickens.

Of course, domesticated chicken continued to be bred in other parts of the world. After the voyages of exploration, the Portuguese brought back domesticated chicken breeds from India. They quickly spread across Europe and replaced all other poultry as the primary domesticated fowl. The main reason for this was that chicken have the highest feed ratio of any domesticated animal, that is, they produce the most meat per pound of feed given to them. In more recent times, factory farms and newer breeds have upped the ratio even more in favor of chickens.

One partial exception is the Americas. Chicken are not native to the new world, and while the early settlers brought chicken with them when they arrived, they found another bird which had already been domesticated by native Americans that was widely available - the turkey. So in the Americas, both chicken and turkey co-dominate.

EDIT: Forgot to add a reference. Most of this stuff comes from the book Why Did the Chicken Cross the World? The Epic Saga of the Bird that Powers Civilization by Andrew Lawler.