Changes in the x-ray orientation factor (a measure of the preferred orientation of cellulose crystallites within a fiber) with time for cotton textiles have been investigated as a possible dating method. The x-ray orientation factor was measured by diffraction of copper K radiation in a textile goniometer for three groups of textiles: one of modern cottons, a sample of curtain from about A.D. 1750, and a group of samples form the 11th-12th centuries A.D. The factor in question decreases with time as a result of crystallite realignment during oxidative degradation, leading potentially to a novel dating method for textiles. -- AATA