Abstract: A 3-term arithmetic progression of a graph is a set of vertices, {u, v, w}, such that dist(u,v) = dist(v,w). A set is called rainbow if no two elements in the set are assigned the same color. In this talk, we will discuss the minimum number of colors needed to guarantee that a graph has a rainbow 3-term arithmetic progression. This is an extension of work done on rainbow arithmetic progressions in the integers and finite abelian groups.