As the biggest fast-food chains have expanded menus to attract new customers, Chick-fil-A Inc. has gained ground with a different strategy: its focus on chicken sandwiches.

Since its founding in Atlanta in 1967 by entrepreneur Truett Cathy, Chick-fil-A’s signature item has been its breaded chicken-breast sandwich served with pickles on a buttered toasted bun. The company sells breakfast and salads, too, but its relatively simple menu stands out, compared with its fast-food rivals.

Now, five decades later, the closely held company this year is poised to become the third-biggest U.S. restaurant chain by sales behind McDonald’s Corp. and Starbucks Corp. , according to food-service consultancy Technomic Inc. The growth reflects Chick-fil-A’s expansion over the past decade, as well as consumers’ broader turn toward chicken.

“We’ve been pretty consistent in how, over multiple decades, we’re going to take it slow and steady,” Mark Moraitakis, a Chick-fil-A senior director, said about the company’s expansion. “It’s paid off for us.”

Sales from Chick-fil-A’s restaurants have tripled over the past decade, reaching $10.2 billion last year, Technomic said, even though the chain is closed on Sundays, a practice implemented by its conservative Christian founder.