Ahold Delhaize has a small line of stores called bfresh, at the moment they have three locations in Allston, Brighton, and Somerville, MA.
"bfresh® offers more natural and organic options than a typical supermarket, as well as vegan products, gluten-free options and specialty products."
http://bfresh.com/
Seems like they are trying to go after the whole foods / trader joes / moms market type of store, not exactly the type of place I would shop but it seems interesting anyway.