The Pinnae (leaflets) alternate, the sporangia look to be round and in two straight rows of four on the pinnules. The stem is not red so it's probably not a Lady Fern.
My guess is Dryopteris. As tx_flower_child said a Wood Fern or (if the fronds begin yellow/orange/gold then turn green) an Autumn Fern is a strong possibility.
The picture on the Missouri Botanical garden page of D. erythrosora looks similar to me.
http://www.missouribotanicalga...
I will look through my fern books to see if there are other possible ones. Certainly I defer to anyone who know ferns; I love them, have quite a few varieties, but certainly won't claim to be an expert.
