People have been eating eggs since there first started to be people, about six million years ago. Eggs have a lot of protein in them, and they don't fight back - you can get them just by climbing to where the nest is and picking them up.
All through antiquity and the Middle Ages, right up until modern times, chickens only laid eggs for part of the year - mainly in the spring, when there was plenty of daylight but it wasn't too hot out. That's why we have Easter eggs and the egg on the Seder plate - to celebrate the return of eggs in the spring. A lot of traditional egg recipes call for other foods that are in season in the spring, like chives or mushrooms or asparagus.
(Today chickens lay eggs all year round because farmers keep them inside in big barns with electric lights and air-conditioning so they can control the temperature and the amount of light.)
The earliest way to eat eggs was raw, but once people began to use fire, about a million years ago, they often roasted eggs in the coals. With the invention of pottery, about 5000 BC, boiling eggs gradually became more common. In ancient Rome, hard-boiled eggs were so common as an appetizer that people said "ab ova ad mala", from eggs to apples, meaning from the beginning of the meal to the end, or from start to finish. People also began to use eggs in breads, cakes, and custards.
Eggs would keep for only about a month before you had to eat them. To make them keep longer, people would often pickle eggs in salt water and vinegar. In China, people fermented eggs to make them keep longer. They called this "thousand-year-old eggs" but they are really only a few weeks or a month old.
(You don't have to refrigerate eggs unless you wash them; in the United States our eggs are washed, so they do have to be refrigerated.)
To find out more about chickens, check out these books from Amazon.com or from your library:
Chicks & Chickens, by Gail Gibbons (2003). Explains where chickens come from, and what they eat, and so on. For younger kids.
A Chicken in Every Pot: Global Recipes for the World's Most Popular Bird, by Kate Heyhoe (2003). Includes a brief history, and lots of recipes for chicken.
Much Depends on Dinner: The Extraordinary History and Mythology, Allure and Obsessions, Perils and Taboos, of an Ordinary Meal, by Margaret Visser (1999). Background on what you eat, including a chapter on chicken.
Food in Antiquity: A Survey of the Diet of Early Peoples, by Don and Patricia Brothwell (1998). Pretty specialized, but the book tells you where foods came from, and how they got to other places, and what people ate in antiquity. Not just Europe, either!