Chickens and mulched beds are the same as cats and a sandbox - irresistible attractions.
Deer netting, a tough plastic alternative to chicken wire can be laid down over mulch. As the plants grow, you will need to rig the netting or wire into a vertical fence. It needn't be high, two or three feet is adequate. Chickens won't try to fly over something unless there's a solid place to land on top to enable them to jump down from.
However, as I watched one lazy afternoon, content in the knowledge I had protected my planting beds with a chicken-proof barrier, a small but determined hen proceeded to dig a hole on the outside of the fencing, and in just a minute an a half, she was under the fence and inside, triumphantly tossing mulch and newly rooted plants every-which-way.
My hens don't free-range now during growing season.
By the way, I use electric wire to keep out bears from my gardens, but the hot wire doesn't seem to phase the chickens at all when they brush up against it.