Can anyone help me out with this wild flower? It grows in rich soil, part shade, and the flower never seems to open any more than in the picture. I thought it might be a green Uvularia but can't find any information on it.

It certainly looks like Uvularia. I don't see any flower buds, only leaves unfurling.
The species that occur in your state are U. grandiflora, U. perfoliata, U. puberula, and U. sessilifolia.

Here's the key to Uvularia... you may be able to figure it out without delving too deeply into these details, though:
http://www.efloras.org/florata...

Other possibilities include solomons seal (Polygonatum sp.) and false solomons seal. (Maianthemum racemosum)

I suspect the latter.

Edit:
Just checked Uvularia sessilifolia... looks like maybe a better match...

I wish I could help with this one, but have no idea.

I'd agree with Sessile Bellwort (Uvularia sessilifolia):

Merrybells (Uvularia sessilifolia)

If you look at the picture you can see the flower is green and hanging down right in the center of the picture. Maybe this year it will be a different color say more greenish yellow. I'm with Uvularia sessilifolia except for the color. Thanks for all your help. I'll post a picture when it is in bloom.