The north rim of the canyon has quite a lot of bare rock--acres and acres of horizontal surface. It only rains about 8 inches a year there, but when it does rain, all the rain that hits the rock of the north rim runs off. The Chacoans had developed an elaborate irrigation system that was able to capture and channel this runoff, effectively doubling the rainfall available to them during the growing season. Also, there was a dam at the end of Chaco Wash (supposedly a natural sand dune, but I am skeptical)from about 900 AD until about 1020 AD, which raised the local water table quite a bit.
The corn they raised was probably similar to Hopi corn. The Hopi plant their corn very deep...about 8 inches...and the corn has a taproot, which goes very deep for water (unlike most corn, which has a shallow fibrous root system). The Anasazi were able to stretch their meager water resources very far.
Most of Pueblo Bonito appears to be composed of storehouses, which has led some archaeologists to surmise that Chaco was a regional storage and distribution center for the Anasazi, so that when food was plentiful in one area, the excess could be stored there; and when another area was experiencing famine, people could come to Chaco for relief.
Also, many of the plants in that "barren" area are edible. I bought a book on the plants of the Four Corners area, and was amazed to find that the Navajo use almost every one for either food, drink, or medicine.
Yes, they were a fascinating people. Have you read Louis L'Amour and Tony Hillerman, both of which know much about the anasazi. They were geniuses at capturing water--absent that they would have perished look before their time.
Speaking of corn...the first time I visited Mesa Verde (many moons ago), we were told that viable corn seed had been found in the ruins. At that time, there was a patch of corn growing that had resulted from the original find of seeds.