A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in where is an n-dimensional projective space. To define the Chow coordinates, take the intersection of an m-D algebraic variety Z of degree d by an -D subspace U of Then the coordinates of the d points of intersection are algebraic functions of the Grassmann coordinates of U, and by taking a symmetric function of the algebraic functions, a homogeneous polynomial known as the Chow form of Z is obtained. The Chow coordinates are then the coefficients of the Chow form. Chow coordinates can generate the smallest field of definition of a divisor.