According to various sources, the cheapest grocery stores in the United States are:

1. Aldi: This German-based company is considered one of the most popular grocery stores in the country, offering top-tier product quality and affordability.
2. Woodmans Markets: This chain offers great prices by not carrying every variety and brand of every grocery item.
3. WinCo Foods: This employee-owned company offers low prices by keeping overhead costs low and buying in bulk.
4. Lidl: This chain offers great prices by not carrying every variety and brand of every grocery item.
5. Market Basket: This New England-based chain was named the "top grocery retailer for inflationary times" by a recent study.
6. Grocery Outlet: This chain offers discounted products by purchasing overstocked or discontinued items from other stores.

Its worth noting that the cheapest grocery store may vary depending on location. For example, Walmart was found to be the cheapest grocery store in Eugene, Oregon. Additionally, some stores may offer lower prices on specific items or brands, so its important to compare prices and shop around to find the best deals.