I took a few quick pictures, and then we went inside. I did a few chores, and then I went outside again and the butterfly was in the same position. Here's a view in slightly different light:
Without my books, it's harder to identify things. I searched on the Internet, and I'm guessing this is a Common Checkered-Skipper (Pyrgus communis), but let me know if you think it's something different.
While scanning pictures and information about Common Checkered-Skippers, I ran across this description from butterfliesandmoths.org: "Adults roost exposed on a tall plant beginning in late afternoon."
This meant that the butterfly might spend the night in that location. So I went out again after dark, and it was still there!
I liked this head-on view:
Perched on a flower seems like a nice way to spend the night!