Locate the desired planting site for the chilopsis, which should have full sunlight and soil that does not puddle immediately after watering or rainfall. Chilopsis can grow in a variety of soil types, including clay.
Position a garden tiller at the edge of the planting site and set the blade adjustment to at least 6 inches deep. Put on safety glasses and a dust mask. Turn the tiller on and push it back and forth over the site to loosen the clay up.
Spread 3 to 6 inches of course sand or compost over the site using a shovel and making it as even as possible. Although compost provides extra nutrients, the chilopsis does not require it so using sand works just as well to increase drainage in the clay.
Work the organic material into the soil by increasing the blade depth on the tiller to 12 inches and pushing it over the planting site again.
Dig a hole in the area that is the same size as the plastic pot that the nursery planted the chilopsis in. Remove the chilopsis roots from the pot and center them in the hole. Back fill the remainder of the hole with the clay soil mixture and pat the top of it with your hands.
Water the soil around the base of the chilopsis to a 5- or 6-inch depth. After planting, reduce watering to only when the top 2 to 3 inches are dry.