No. The Church of Jesus Christ of Latter-day Saints (the “Mormon” church) has never owned or operated a grocery chain. The closest thing to a grocery store that is operated by the Church is called the ‘Bishops Storehouse’, it is a mix between a food pantry and a grocery store. The items at the Bishop’s Storehouse are only distributed to those in need who have been referred by a Mormon Bishop.
While the church doesn’t own a grocery chain, this doesn’t mean that members of the church haven’t or can’t own a grocery chain. However, this does not equate to The Church of Jesus Christ of Latter Day Saints owning a grocery chain.
An example of a member of the church owning a grocery chain is the food chain Smith’s which started in Brigham City, Utah and was owned by Lorenzo J. Smith and by his Son Dee Smith, who was a great nephew of Joseph Smith Jr.