  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 $\mathfrak{p}$ of $M$ such that the
stable reduction of $C$ at $\mathfrak{p}$ contains three irreducible components
of genus $1$.
