The legs and runners of the coop are made from pressure treated wood. They are fine to be in direct contact with the ground. Both grass and ground are good surfaces to place your coop on. The ground under the coop should be level. It is essential for both the longevity of your coop and for the health of your chickens that water should run away from the coop and run.
Preparing the Ground for a New Chicken House
Preparing for delivery may be a whole lot easier than you imagined. Your new coop only requires a flat, well-drained surface to sit on. The grass is fine. Water should not drain towards it or pool around the bottom of the coop (that would be harmful to your chickens as well).
The pressure-treated legs and runners will last for years and years on the ground without anything else under them. If you prefer for your coop to sit on a base - cinderblocks, gravel, or concrete is fine. The primary concern is prolonged exposure to moisture so water must have an escape and it must not collect around the base of the coop. See, easy breezy!