We consider Lorentzian wormholes with a phantom field and chiral matter fields. The chiral fields are described by the non linear sigma model with or without a Skyrme term. When the gravitational coupling of the chiral fields is increased, the wormhole geometry changes. The single throat is replaced by a double throat with a belly inbetween. For a maximal value of the coupling, the radii of both throats reach zero. Then the interior part pinches off, leaving a closed universe and two (asympotically) flat spaces. A stability analysis shows that all wormholes threaded by chiral fields inherit the instability of the Ellis wormhole.