You can have your groceries delivered with Instacart. Right not they are offering free credit and free delivery for joining.
Get a free $10 credit to Instacart. Join here and your first order will be delivered free as well. It should add the code when you sign up, if not use code MHENRICKSON12716B
Depending on your area you will see which stores are available. It just launched in my area, it may not be offered in all locations.