It may be time for bruised and battered Chipotle (CMG) - Get Report to rally behind the vision of a single leader. 

The better-burrito joint has had a co-CEO structure since promoting Monty Moran from President and Chief Operating Officer in January 2009 to serve alongside founder Steve Ells. Moran, a lawyer by trade and long-time friend of Ells, was there at Chipotle's founding.

As is recalled fondly on the website of Moran's former employer Messner & Reeves, one day back in the early 1990s Moran was asked by Ells to sample a new burrito recipe. Moran allegedly tasted the creation and promptly said, "You out to sell these things." 

Ells wasted no time taking his bestie's advice. In 1993, Ells took his recipes and opened a small burrito joint in Denver, Colo. By 1997, with five stores up and running, Ells reportedly reached out to Moran -- who was practicing law at Messner & Reeves -- for business and legal advice. 

After Moran had led so much of Chipotle's strategy over the years, the website says, he joined Chipotle as President and Chief Operating Officer in 2005. And, on Jan. 26, 2006, Moran found himself ringing the bell to open trading at the New York Stock Exchange as Chipotle became a public company. Since then, many on Wall Street have held that Ells -- a classically trained chef -- was in charge of Chipotle's push to source better ingredients, while Moran handled operations, growth plans and developing what it calls a "unique people culture."

But, it hasn't been made clear to investors why Chipotle needs to still have such a co-CEO structure. In fact, if anything, Moran should be the fall guy for Chipotle's food safety scares in 2015 due to his focus on operations. Acording to Chipotle's website, the company doesn't have the chief operating officer role that is common in restaurant chains. Ells is unlikely go anywhere, seeing as he is the founder, face of Chipotle, and architect of the company's menu.  

"It's certainly an unusual arrangement, and it's never been clear why Chipotle needs a co-CEO structure," says CtW Investment Group lead analyst Derrick Wortes. CtW Investment Group and Amalgamated Bank recently jointly filed a shareholder proposal against Chipotle to remove Ells as chairman and replace him with an independent director.

Severing ties with Moran would at least help Chipotle improve some of the optics around its excessive CEO compensation.

"One of the main reasons why Chipotle's executive pay figures were so astronomical (when we first approached them with that critique in 2014) was precisely because they're paying dual CEOs," Wortess explains. Ells earned $13.8 million in total compensation in 2015, down from a jaw-dropping $28.9 million in 2014. Moran saw his total compensation decline to $13.6 million in 2015 from a whopping $28.1 million the year before.

Chipotle may want to take a page from  Whole Foods (WFM) ahead of 2017, which has made efforts of late to bolster corporate governance. The struggling organic grocer recently said co-CEO Walter Robb will leave his position by Dec. 31. Robb has been co-CEO with Whole Foods founder John Mackey for the past six years. He has spent 25 years at Whole Foods, and was an integral player in growing the company from 12 stores to 464 stores in three countries.

He will remain on Whole Foods' board and serve as a senior adviser to the company.

Wortes said, "We're presently focused on the independent chair proposal and have not engaged the company around breaking up with the co-CEO structure. But the news on Whole Foods gives everyone -- owners and managers -- something to think about."

Chipotle did not return a request for comment.