So I had no choice but to bathe her. I didn't think soap would be a wise idea so I just held her carefully under a stream of warm water until she was pretty clean. She objected a little but not much. I toweled her off and then dried her the rest of the way with a hair dryer on low. I assumed she would hate that part but in the end I think she liked warm air, especially under her wings.
I refrained from singing "Wind Beneath My Wings"... ;) She's clean now and in the brooder under the light with a buddy. The rest if the babies are outside today stretching their wings and enjoying 75 degree weather. I'll send her out once I'm sure she's not going to get chilled.
(And side note, we really dont know yet if this chick is male or female. We're just telling them all they are girls and that if they crow, they go...)