The only plants my chickens have not destroyed are the daylilies, a small New Jersy Tea shrub, and yarrow. The daylilies and yarrow would do fine in the shade.
However, I think one of the reasons the daylilies have been left alone is that they are planted up against the garage in such a way that it may be difficult for them to dig around them. The yarrow, on the other hand, is easily accessible but completely ignored.
I was actually quite surprised that the lily of the valley succumbed to the chickens. That is a poinsonous plant, but they pecked at it so much it finally gave in. Other shade loving plants they tore up include bleeding heart, pulmonaria, and lady's mantle. Again, I don't think they ate the plants, but their constant scratching and tromping on these plants likely led to their demise.
I'm waiting to see how the star of bethlehem (considered an invasive weed in some areas), grape hyacinths, and tulips survive the chickens in the spring!