The chromatic index of a graph G, χ'(G), is the least number of colors of some edge coloring of G such that no two adjacent edges have the same color. Given a graph G and an integer k, to decide if χ'(G) ≤ k is NP-complete. A graph is an interval graph if it represents the intersection relation of a set of closed intervals in R. A graph is a split graph if its vertex set can be partitioned into a clique and an independent set. A graph is split-interval if it is simultaneously an interval and a split graph. In this paper we show how to determine the chromatic index of all split-interval graphs. Our proof leads to a polynomial-time algorithm to deciding if χ'(G) ≤ k given an integer k and a split-interval graph G.