Since going public on July 25, the company has seen its shares soar about 140 percent, making it the fourth best IPO of the year.
The key to El Pollo Loco's success is its "unique" Mexican-themed menu—which is centered around its signature grilled chicken—and its positioning between traditional quick-service and fast casual restaurants, Sather said.
Read MoreBurger flippers earn the least here
El Pollo Loco's food is "much like the quality of food you'd find at a Chipotle or a Panera—the fast casual at the high-end—but we offer the speed, convenience and value that you'd find at quick service," he noted.
While there are currently 401 El Pollo Loco locations situated in the Southwest, the company is looking to eventually open 2,300 restaurants across the country.
Read MoreHere's your chance to win a lifetime of Taco Bell
"We are very excited about our expansion potential," Sather said.
In fact, the company is currently hiring for its Houston store, which is expected to open in October.
—By CNBC's Michelle Fox. CNBC's Stefanie Kratter contributed to this report.