2024 could bring Louisiana-style fried chicken to Saugus, as the rapidly expanding fried chicken restaurant chain Raising Cane’s seeks to open its fifth Massachusetts location in town.

The Saugus Board of Selectmen will vote Tuesday whether to grant the owners of 799 Broadway a special permit, allowing them to open a Raising Cane’s restaurant with a drive-thru booth at the location.

Currently, Raising Cane’s, which specializes in cooking what it claims are “the most craveable chicken finger meals” around, has two franchises in Boston along with locations in Methuen, which opened in October, and Marlborough, which opened in May. The Marlborough franchise’s opening attracted such a large crowd of customers that Marlborough Police officers were brought in to direct traffic near the restaurant.

Since Todd Graves founded the restaurant in 1996 in Baton Rouge, La., Raising Cane’s has expanded to more than 500 locations in the country, along with a few overseas.

“Since day one, our vision is to have restaurants all over the world and to be the brand for quality chicken finger meals with a great crew, cool culture, and active community involvement,” the Raising Cane’s website reads.

This summer, Raising Cane’s opened its more than 8,000-square-foot flagship restaurant in New York City, claiming to be “the largest restaurant in the bow tie of Times Square.” According to the online food publication “Eat This, Not That,” the chain’s fast and consistent expansion could make it a top-10 fast-food chain in a few years.

“We’ve grown a lot over the years (thank you very much), and we’re excited for the opportunity to experience growth through the growth of our communities,” the Raising Cane’s website reads.