On their arid, windswept reservation at the corner of Arizona, Utah, Colorado and New Mexico, the Navajo Indians dragged on for generations in disease-ridden, edge-of-hunger poverty. Untrained for the fast changing white men's world, they seemed resigned to everlasting subsistence-living and stagnation. Then, a year ago, money began flowing in as U.S. oil companies scrambled for gas and oil leases in the Southwest's vast Paradox Basin, much of it lying in the Navajo and Ute reservations.
By tradition and legend, poverty-gnarled Indians who suddenly come into oil money—as in Oklahoma in the 1920s-throw it around in wild spending sprees, and...