In 2000 Kapovich and Kleiner proved that if G is a one-ended hyperbolic group with 1-dimensional boundary, and G does not split over a two-ended subgroup, then the boundary of G is either a Menger curve, a Sierpinski carpet, or a circle. Kim Ruane has asked if there is a CAT(0) generalization of Kapovich and Kleiner’s theorem. As boundaries of CAT(0) groups are in general not locally connected, there is no hope of such a generalization for general CAT(0) groups. However, a version of Kapovich and Kleiner’s theorem may hold for certain classes of CAT(0) groups. In this talk I will discuss a generalization of their theorem for CAT(0) groups with isolated flats.