J.C. Penney (OTC:JCPN.Q) has a leadership problem. The company's former CEO, Marvin R. Ellison, left the company in late May to take the top job at Lowe's (NYSE:LOW).

Ellison's leaving may not have been a comment on how he views J.C. Penney's future. He has a strong background in home improvement having spent much of his career at Home Depot, where he led store operations in the United States. Going to Lowe's may have just been a chance to take a bigger job in a field where he has a high level of comfort -- and is not as affected by the so-called retail apocalypse.

Still, it's hard to imagine that potential successors won't at least consider whether Ellison left because he believed the company wasn't going to make it. Being Lowe's CEO is a better job than being J.C. Penney CEO -- arguably a dream job for Ellison -- but being the man who saved an American retail icon would have been an impressive calling card as well.

The exterior of a J.C. Penney store

The new J.C. Penney CEO stands to inherit a host of problems. Image source: J.C. Penney.

Where is J.C. Penney now?

After Ellison left, lead independent director Ronald W. Tysoe took over as chairman of the board. The company also created an office of the CEO consisting of Chief Financial Officer Jeff Davis, Chief Customer Officer Joe McFarland, Chief Digital Officer Therace Risch, and Executive Vice President of Supply Chain Mike Robbins.

"These four leaders will share equal responsibility for the Company's day-to-day operations until a new CEO is appointed," according to a press release. A search committee is looking for a new CEO, and you have to assume some of those mentioned will be considered, though the company has not confirmed that. 

This uncertainty comes at a time when J.C. Penney has had some positive signs in its recovery, but it has most certainly not turned the corner. In the first quarter, there were reasons for both encouragement and pessimism. Total sales decreased by 4.3%, which the company largely blamed on its strategic store closings. Comparable-store sales, however, rose by 0.2%, which is a strong positive.

Who would want this job?

J.C. Penney lost a potential interim candidate when its two-time CEO Mike Ullman took over for Howard Schultz as chairman of Starbucks' board of directors. He has twice previously led the retailer and has shown himself to be competent, albeit not overly dynamic.

The list of executives who have successfully guided a retail chain through a turnaround is short. It's hard to see Hubert Joly leaving Best Buy and it's unlikely that former Domino's CEO and savior Patrick Doyle would want to take on a challenge as big as J.C. Penney.

Calls should be made to both of those men just in case they want to try their hand at something new. Perhaps one of them wants to be Theo Epstein, the baseball executive who became a hero leading Boston to a World Series win and became a legend when he did it again with the Chicago Cubs.

If those efforts fail, J.C. Penney's search committee should look to executives of successful retailers ready to be a CEO. That might mean someone from Walmart digital boss Marc Lore's leadership tree, or perhaps someone working under Target CEO Brian Cornell.

What is the risk?

The next J.C. Penney CEO will almost certainly be a less-than-sure thing. He or she will either be new to the top job or someone whose experience in the top position is unrelated to retail. That can work -- Joly came from the hotel and travel space -- but it adds a layer of uncertainty to a company that already faces significant risk.

Ellison pointed J.C. Penney in the right direction, but hurdles remain. Whoever gets named the company's new CEO won't just have to steer the ship straight ahead. He or she will have to make some hard choices at a company with very little margin for error.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.