I'm in a suburb close to Chicago. Grocery stores are everywhere and extremely competitive. As a frugal guy, I'm just naturally motivated to take advantage of that. We get a "shoppers newspaper" which includes flyers from most of the stores in the mail on Wednesdays. By skimming the flyers and being willing to shop 4 - 5 stores, I seldom buy groceries that aren't on sale, frequently deep sales.
to beating the deals I can get by shopping the loss leaders at several independent or chain groceries. WM and Target have overall good prices but few really deep discounted sales.
Hope you're are smart shopper and really check out those flyers. We have an Albertson's that's always running the "buy one get one free". They always say how much you are saving but most of the time it's what I get it for at WalMart anyway. Same for Winn Dixie. Not saying they don't offer some good deals but most of the time it's just a come-on.