Are there supermarket chains that are struggling to complete with Wal-Mart Stores, Inc. (NYSE: WMT)? Sure there are, and the case of small-town grocery retailers going up against the Bentonville behemoth is pretty well documented. But, right off the bat, let's scratch one name off that list: Publix Supermarkets.

The privately-held Publix had sales of over $21 billion in 2006 and has just opened up its 900th store. That 2006 revenue level was up 5% from the previous year, and so far, Publix does not seem (or probably feel) threatened by Wal-Mart's grocery efforts, which come in the form of Supercenters and Neighborhood Markets. Add to that tidbits like Publix having a 40% market share in Florida (its home state) and the face that it is actually taking business from Wal-Mart in its new markets of Alabama, Georgia, Tennessee and South Carolina, and it has to be asking itelf: "do you feel lucky?"

Where is Publix getting its mojo from? Customer satisfaction? Check. Publix ranks number one on the American Consumer Satisfaction Index. Publix take your groceries to the car and refuse tips -- and they also own 31% of the firm through an employee share-ownership plan. This is no Wal-Mart. Want more proof? Publix began selling organic and natural products in 1996 -- Wal-Mart began selling organic food only last year, and rumors continue that it may be retrenching into those organic plans a bit (although I've seen no proof of this yet).

Let it be said here for those who find it hard to believe: Yes, it is possible to compete against Wal-Mart ... and win.