Houston franchise owner Joseph DeCola saw the device while on his honeymoon at the Four Seasons in Maui and decided to install it in his location. Devin Deshotel, an area manager, installed them in two other Texas locations in Wallisville and Uvalde.

Chick-fil-A is experimenting with Kallpod, a small device that sits on its dining tables and summons a server whenever it's pushed, kind of like ringing a bell for a butler. Service staff members get an alert on their smartwatch to assist customers with questions, filling a second food order or to request a manager.

However, the company is trying to incorporate technology in a way that elevates its hospitality, not replaces it, and bolsters sales.

Stepping into the iconic red and white buildings, customers find a menu board of chicken sandwiches and waffle fries and not a single digital ordering kiosk in sight. The privately held chicken restaurant is known for its customer service and quality ingredients, often shunning over-the-top, limited-time offers and technology in favor of a simple menu and personal service.

In a sea of burger chains and taco joints, Chick-fil-A stands out in more ways than one.

It's just in three locations, but Deshotel said the results are staggering. Not only did hospitality scores from its customer surveys go up, but so did sales.

"It's all about the experience of the guest," Deshotel told CNBC. "Of course, greater financial returns are great, but that wasn't the thought process when getting [Kallpod]. It was always about continuing to provide a remarkable experience."

The Wallisville location is the chain's second-busiest Chick-fil-A, out of more than 2,200 locations. Deshotel said its revenue rose 500 percent after installing the Kallpod, because it gave diners an easier way to place a second order. About 4,000 customers walk through the door of this restaurant every day and it garners $10 million per year in revenue, Deshotel said.

Initially, Deshotel's two restaurants had employees walking around with iPads to take second orders and averaging $30 to $45 a day in extra sales. After adding Kallpod to the tables, the restaurants averaged an extra $200 to $350 per day in second orders.

This additional revenue more than paid for the extra labor Deshotel added to each shift to cover the new service. He said the majority of orders were for inexpensive items like ice cream or milkshakes.

"We wanted to create a platform that did two very simple things," Steven Barrow Barlow, chief operating officer of Kallpod, told CNBC. "Firstly, technology that reinforced the human element of the service experience. Simply, something that increases human interaction and doesn't remove the human ... secondly, guest-facing technology that aesthetically looked good and doesn't bring down the experience."

Currently, the first generation of these devices run on radio waves, but the second generation will be Wi-Fi-based, he said.

"When we launched [Kallpod], I presumed this would be a tool that bar and grill, full-service casual diners would embrace first and the fastest, but kind of surprisingly it was embraced more quickly by higher-positioned hotels," Barlow said.

The company currently has products in more than 600 venues including hotels, luxury boxes in stadiums and amphitheaters, as well as restaurants.

While Chick-fil-A restaurants are individually owned and there is no plan to add Kallpod to all of the company's locations, Deshotel said there is already interest among other owners to bring the technology to more stores.