Only one Washington-area business devotes itself entirely to selling children's books: The Cheshire Cat, located three blocks south of Chevy Chase Circle on Connecticut Avenue.That would seem to be a narrow focus for a thriving D.C. retail concern, but since its opening in mid-September 1977 -- with Amy Carter as a first-day customer -- Cheshire Cat has done considerably better than even its four owners expected.

Charlotte Berman, Helen Neuberg, Pamela Sacks and Jewel Stoddard were formerly colleagues at a well-known, suburban private school. After deciding to leave teaching and administration, "We insisted on staying together and providing an educational service," Stoddard says. Even though none of the four had business experience, they began investigating the possibility of opening a bookstore for children.

The first problem they encountered was learning about business. The women looked into programs at the Small Business Administration and a local college, "but they didn't offer much, they were too elementary," says Neuberg, adding, "One consultant was going to spend an hour of our time, at our expense, telling us all the reasons we shouldn't open a children's bookstore."

But the women were undeterred. "With the high educational achievement of parents in this area, we were convinced that a store with a wide choice of quality books for children would be well-received," Neuberg says. Many bookstores offered a few popular choices for children, but none had a wide selection or a sales force knowledgeable about children's literature. On the other hand, they wondered why previous attempts to operate such a store had failed. Many bookstores, however, did not offer a wide selection of children's books, nor did they have a sales force knowledgeable about children's literature.

"When I first called on Cheshire Cat a year-and-a-half ago," says Anne Brooks, regional sales representative for G. P. Putnam & Sons, "I assumed they had been in business for years. The people there were so professional and they knew so much about children's books."

But knowing about books is not enough to ensure a healthy profit. For example, a fine children's bookstore in Gaithersburg, Md., closed primarily because the mall in which it was located was not attracting sufficient traffic.

Harbor Place in Baltimore houses a small children's bookstore, and one is expected to open soon in Annapolis. But such stores' staying power has been poor. Even in Manhattan, only one children's bookstore survives.

Cheshire Cat, however, has thrived. While its owners will discuss few financial details, they do concede that, after its first year of operation, sales figures were 150 percent higher than their most optimistic prediction.

"We knew that there was a market for a high-quality children's bookstore," Neuberg says, "and we feel quite certain that it will continue. But, believe me, our success has not been accidental. We've really done our homework."

Before selecting their Connecticut Avenue site, the four women rejected other seemingly choice locations. For example, a site on Wisconsin Avenue in Bethesda was turned down because most stores in the area close after working hours.

The women also insisted on a location close to family-oriented neighborhoods. They wanted as many parents and children as possible to be able to walk from their homes to Cheshire Cat, and they wanted those who could not to have access to long-term legal parking.

The shop's name, too, was crucial. They wanted an easily identifiable one from children's literature. Charlotte's Webb was strongly considered, but its author, E. B. White, wouldn't allow it.

Evidently, the Cheshire Cat's owners made the right choices. Although financial data is secret, sales are in six figures. Sixty-seven percent of its dollar volume is represented by hardback sales, and at any given time, the store is likely to have 5,500 hardbacks and 4,500 paperbacks in stock.

Subjects include fiction, nonfiction, cooking and humor. Most hardbacks range from $2.50 to $16.95, and the average price is about $6.50. Some book sets sell for $40.

Often on Saturday morning, Cheshire Cat presents well-known authors who autograph their books. Youth-market superstars such as Judy Blume, Arnold Lobel and Maurice Sendak have appeared. Each costs Cheshire Cat nothing, with expenses being absorbed by publishers.

According to Berman, Cheshire Cat devotes 2 percent of its annual gross sales to advertising, most of which goes toward printing and mailing its periodic newsletter to 5,000 potential customers.

By any criteria, Cheshire Cat has made it. But although they're afraid success may invite imitation, the owners plan no branches or franchises.