Chow quotients of projective varieties by affine torus actions provide alternative constructions of interesting geometric objects. For example, the moduli space of stable genus 0 curves with nmarked points arises as the Chow quotient of the Grassmannian Gr(2,n) by the n-torus, and the wonderful model of a hyperplane arrangement is the Chow quotient of the matroid Schubert variety by the ℂ∗-action. In this talk, we focus on the Chow quotients of projective varieties by ℂ∗-actions. For toric varieties, the work of Kapranov, Sturmfels and Zelevinsky shows that the Chow quotient is another toric variety associated with the fiber polytope. Extending this perspective, we demonstrate that, under certain conditions, the local geometry of the Chow quotient is governed by a toric variety. As an application, we establish rational smoothness criteria for Chow quotients of Schubert varieties by ℂ∗-actions. This is joint work with Mateusz Michalek and Leonid Monin.