There were a LOT of these during the dot-com hype years, Peapod, NetGrocer, WebVan, etc. etc. (even Kozmo.com), and most have died out or like Peapod, gotten purchased (after hobbling near bankruptcy many times) by a larger retailer.
There is a lot of potential to this, but the biggest problem of which is logistics. Do you set-up your own warehouse? Do you partner and shop via another store (from which you have to put your margins on top of it), how do you deal with orders when customers aren't at home when your delivery person arrives, etc. etc.