Let C be a smooth, absolutely irreducible genus-3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1. Joint work with Bouw, Cooley, Lauter, Manes, Newton, Ozman.