The spinor variety S_n is a Lie-type D analog of the Grassmannian.  We will discuss the initial degenerations (degenerations arising from Groebner theory) of the spinor variety and show how they are related to (valuated) even Delta-matroids. As an application, we will study the birational geometry of the Chow quotient of S_n by the maximal torus of O(n), with a particular emphasis on n=5.