Lucrezia Borgia, named after a 15th-century Roman beauty, has a white crest that falls somewhere between a mohawk and a bouffant. There is a trio of Polish chickens named Zsa Zsa, Eva and Magda, after the Hungarian-American Gabor sisters. And there are three all-black Swedish chickens: a rooster called Mac Daddy, as well as two hens named Ruby Woo and Lady Danger, after lipsticks sold by MAC Cosmetics , the Estée Lauder Cos. unit with an all-black dress code where Ms. Tetzlaff works.

“Chickens are beautiful, and I never knew that,” said Ms. Tetzlaff. Visitors to their Pennsylvania farm are amazed to learn the birds are all just varieties of chicken, she adds.

Yes, backyard chicken coops have long been a thing. That’s why people are moving on to specialty breeds of all shapes and sizes that sport outlandish plumage, lay colorful eggs or have appealing personalities. “Boutique” chicken companies are scouring the world for unusual types, creating new hybrids or promoting heritage American breeds to feed demand.

Silkies have fluffy plumage like Big Bird and blue earlobes. Polish Frizzles are nicknamed “pine cone” chickens because they resemble giant ones. Cochins look somewhat like feathered basketballs.

“It’s like orchids or tape measures or any other weird thing that people collect,” says Paul Bradshaw, whose Greenfire Farms, in Havana, Fla., is a supplier to what he calls the “ultra-exotic premium chicken market.”

As commercial chicken production took off in the U.S. in the 1950s, the number of so-called heritage breeds dwindled in favor of a few fast-growing hybrids, which usually have white or reddish feathers and lay white or brown eggs.

But chickens, like dogs, have “wildly varying looks, as between a chihuahua and a Newfoundland,” says Mr. Bradshaw. He says his typical customer is a woman between 35 and 65 years old, “with a college degree, quite a bit of disposable income, who likes to garden.” Rare chickens are like folk art, he says. Customers see them as embodiments of a simpler time.

When Mr. Bradshaw first imported an Indonesian breed called Ayam Cemani, three years ago, a breeding pair sold for about $5,000. These chickens have black feathers, beaks, combs, tongues, skin, organs, bones and meat, but lay white or cream-colored eggs.

He also sells Liège Fighter chickens such as Jesus, which can cost as much as $199 for a day-old chick. Another tall breed, the Shamo, which costs $59 and is originally from Asia, is “like having your own pet velociraptor.”

 

By contrast, day-old chicks of more common breeds cost just a few dollars.

In November, more than 5,000 birds will compete for the title of Super Grand Champion at the Ohio National Poultry Show, sometimes called the Westminster for chickens. Show birds are judged on how well they match up to the American Poultry Association’s “American Standard of Perfection,” a 143-year-old publication.

In a 2014 survey of backyard flock owners published in the journal Poultry Science, 57% said having the birds as pets was one of three major reasons for keeping chickens. The other two were for eggs or meat, and for pest control in the garden. People also said they enjoy watching their chickens’ behavior.

 

Texas farmer David Bailey breeds thoroughbred horses, but he began breeding chickens on the side, saying he hopes to help preserve genetic diversity. In the process, he discovered chickens have “big personality… they expect to be picked up and petted.”

One of his best sellers is the Swedish Olandsk dwarf chicken, roughly the size of a grapefruit, which lays white eggs “the size of a teaspoon.” City dwellers like their size and will often bring them indoors at night, he said.

Backyard efforts have helped improve the status of breeds that could otherwise have become extinct, according to the Livestock Conservancy. The nonprofit’s conservation priority list includes 53 heritage chicken breeds, drawn mostly from a list the American Poultry Association began defining in 1873.

 

About 38 of those breeds are endangered, said Jeannette Beranger, a senior program manager at the conservancy. She clucked at the notion of keeping chickens as pets: “That’s not a career for a chicken.” Instead, she suggests backyard flocks be put to work, either as egg-layers, meat providers or for pest control.

Kelly Pietro, a 39-year-old mother of two in Monroe, Conn., acquired a brood of seven unusual chickens two-and-a-half years ago as a birthday present. To get the perfect combination of birds, Ms. Pietro created a spreadsheet that listed her and her husband’s favorite birds, the color of their feathers and eggs, ranked their docility and whether they laid eggs in winter. Her flock includes Speckley, a dark brown Speckled Sussex chicken with bluish dots, and Ollie, who lays olive eggs.

“It felt like old-school stock trading,” Ms. Pietro said. Her flock produces as many as seven eggs a day. When the family car pulls up, the chickens will come up to the driveway to greet the Pietros, she said.

Traci Torres, chief “eggsecutive” officer of Mypetchicken.com, says her company focuses on breeding chickens that will lay blue, green, chocolate-colored or speckled eggs, which are all the rage around Easter.

Ms. Torres said customers are willing to wait twice as long and pay nearly twice as much for unusual birds or egg layers. She also crossbreeds chickens and is planning a “profusely feathered” one for next year with feathered feet and a cheek tuft, nicknamed the Yeti.

“There are people who go out to their backyard with a glass of wine, feed their chickens mealworms … the chickens will fall asleep in their laps,” said Ms. Torres. “Chickens are a really nice antidote to today’s technology-heavy culture.”

Write to Anupreeta Das at anupreeta.das@wsj.com