I was going to guess peony, if by "standing alone by itself" you mean it needs no more than one bloom to fill the room with fragrance. However, your information indicates that you are in zone 7, and my research (from the Clemson Extension site) says that peonies may fail to bloom if they don't have winter chilling. That information indicated zones 8 and 9.

When you learn the answer, will you post it here? Inquiring minds want to know!

Old timers say if you can grow apples in your county, you should be able to grow peonies. So, with so very little information to base an answer, I am going to guess gardenia.

Plumeria
Brugmansia
Stephanotis
are all intensely fragrant tropical plants that you couldn't grow (outdoors) in VA
But I think there are gardenia cultivars you can grow in zone 7; ditto for camellia

I think the stand alone by itself may have some significance that we're missing, but don't know what it is.

Amorphophallus

Oriental Lily

Jeanne

Oriental lily was the first thing that came to mind with me, I have no clue what someof the other plants mentioned are. Gardenia will fill a room with fragrance, but doesn't strike me as something that would stand alone. Ok, what is it?
Cheryl

Ok, For any of you interested it was in fact an Oriental Lily, specifically a "Stargazer". Based on the postings and some other research I guessed Oriental Lily and was told "close but what kind?" (Tough crowd). Anyway, thanks for the help.