Let G be a graph with n vertices. Suppose that for each vertex v in G there exists a list L(v) of k colors, such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. A graph G is called a split graph if there exists a partition V = I È K such that the subgraphs of G induced by I and K are empty and complete, respectively. The notion of split graphs was introduced in 1977 by S. Foldes and P. L. Hammer, and these graphs have since received much attention in graph theory. In this paper, we characterize the properties of complete split graphs that are uniquely k-list colorable graphs.