Orchard Supply Hardware (Nasdaq: OSH) began trading Tuesday, after a year-end stock distribution to shareholders of parent Sears Holdings (Nasdaq: SHLD). It wasn't a very promising start: The stock priced at $25 per share at the open and closed at $23.53, down 5.9%.

"Avoid dogpiling on Sears" is a New Year's resolution that will be hard to keep. Just this once, let's break it by noting that once again, Sears Holdings is backing a third contestant in a two-horse race. And so far, it hasn't done too well running Kmart against Wal-Mart and Target or Sears against J.C. Penney and Kohl's.

It's never good to be the third guy in a room with two 900-pound gorillas. In electronics, there was only room for Amazon.com and Best Buy, not Circuit City; in bookstores, it was Amazon and Barnes & Noble, not Borders. It's only dumb luck there's no Amazon for hardware -- yet.

But Orchard is going into a different landscape than Kmart and Sears. While the "home center" lineup -- stores selling everything from lumber to lamps -- is hogged by the big boxes, the hardware store market is still spread among many independent neighborhood stores.

If Orchard stays off the footprint of Home Depot (NYSE: HD) and Lowe's (NYSE: LOW) -- by focusing on rural towns and urban areas where big boxes are sparse, for example -- and takes market share from the mom-and-pops, it has a chance to build a decent growth story when the housing market recovers.

Granted, there are a lot of "ifs" in that story. Orchard is a small company, with only 89 stores in California. That leaves a whole lot of country to cover where its main competitors would be True Value and Ace Hardware -- both merchant cooperatives, not public companies answering to shareholders.

Roll the dice on Orchard?
If you're a small-cap investor and willing to roll the dice on Orchard Hardware's new stock, you're betting on Kenmore and Craftsman, respectable Sears brand names -- in fact, the big draws at Sears stores. Orchard expects to have agreements with Sears to continue selling these products. But mainly you're betting Orchard's management can steer away from the mistakes of its parent.

Morningstar, which lowered its fair value estimate for Sears after the spinoff, noted that Orchard is Sears' higher-margin business and assumed that the hardware chain will show $660 million in revenue this year and about $60 million in EBIDTA "with some improvement in 2012 and beyond."

So far, there isn't much of a market for the stock; analysts aren't following it, and trading volume on opening day was less than 4% of its outstanding shares. On the back of this Fool's envelope, with 4.81 million shares outstanding (according to the Nasdaq), the first-day closing price yields a price-to-EBITDA ratio close to 2. Granted, that doesn't mean much until we see some real earnings numbers after the fourth quarter ends Jan. 31.

The real question for now is: Can Orchard chart its own path away from Sears? There's reason to be hopeful. When Orchard's management began talking publicly in July about the Sears spinoff, Orchard CEO Mark Baker said future plans included opening new stores and remodeling existing ones, as well as testing a new prototype store. That's a break from where Sears and Kmart have been stumbling, as seen in their sales numbers and complaints about dingy stores.

Baker, who joined in March, is a former COO of Home Depot and is saying all the right things. For one, he said he's going to stay out of the path of Home Depot and Lowe's and compete with the smaller players such as Ace and True Value.

If you are a Sears Holdings shareholder who got some Orchard stock in the spinoff, don't rush to cash it in; you're likely to see more upside here than in your Sears Holdings stock. Given Sears' results lately, chances are you've already developed an immunity to bad news.

If Orchard can pull all this off, there are worse bets to be made on the housing market. But just as with the big-box hardware stocks, you will need to sweat this situation out for the next few quarters, hoping the housing market makes a real recovery. The most recent figures for the Case-Schiller Index showed that home prices were down in 19 of 20 cities during October, and while November numbers were shaping up better, they're still scraping record lows as we enter the fourth year since the housing bubble burst, and California is still bringing in the rear of the housing market.

Orchard is not a growth story for the short term, but I believe it still has massive upside potential. If you don't think you have the stomach to wait it out, there is another retailer we at the Fool are hugely optimistic on. In fact, we're so excited about it we've dubbed it "The Motley Fool's Top Stock for 2012." Investors can reveal a retail name with real growth potential by accessing their free copy of this report today.