Principles of classical geometry are applied to kiva architecture in Chaco Canyon. Structural features of these circular buildings suggested that the prehistoric Anasazi may have known how to construct regular polygons. Both structural and quantitative aspects of kiva architecture are examined. Concentric rings of Chaco Canyon's kivas were measured to detect presence or absence of proportional signatures of known geometric designs. A result of this examination suggests that great kiva architects were familiar with a technique known as squaring a circle.