In this article, we propose a shift in race research from a one-dimensional hierarchical approach to a multidimensional system of racial stratification. Building upon Claire Kim's (1999) racial triangulation theory, we examine how the American public rates Asians relative to blacks and whites along two dimensions of racial stratification: racial valorization and civic acceptance/ostracism. Using selected years from the General Social Survey, our analyses provide support for the multidimensional racial triangulation perspective as opposed to a singular hierarchical approach, although findings do not match all predictions by the racial triangulation thesis. Our results also suggest that on average whites are more likely than blacks to have more favorable views of the relative positions of Asians, particularly for family commitment, nonviolence and wealth, but blacks are more likely to assume racially egalitarian views than do whites.