  Up to isomorphism over C, every simple principally polarized abelian variety
of dimension 3 is the Jacobian of a smooth projective curve of genus 3.
Furthermore, this curve is either a hyperelliptic curve or a plane quartic.
Given a sextic CM field K, we show that if there exists a hyperelliptic
Jacobian with CM by K, then all principally polarized abelian varieties that
are Galois conjugated to it are hyperelliptic. Using Shimura's reciprocity law,
we give an algorithm for computing approximations of the invariants of the
initial curve, as well as their Galois conjugates. This allows us ton define
and compute class polynomials for genus 3 hyperelliptic curves with CM.
