I would try rolling the sleeves (scrunched never seems to stay in place for me at least anyway) and tying at the waist over a tee and skirt (or dress), column-of-color style, like suntiger says, almost like a lightweight topper treatment. Tying at the waist and rolling the sleeves helps give it structure. This is definitely a more casual, relaxed piece than we normally see for you, so it is a departure. But I think if you embrace the juxtaposition of this shirt with a dressier piece like a dress or skirt, and add casual shoes (and I like the idea of something more substantial like the oxfords), it could work. How about a statement necklace in the neckline too?
I like chambray shirts and am always drawn to them, but have given a couple away because I find myself not reaching for them much. Too warm in our summers here, and when it cools, I'm eager to wear other more substantial pieces. But I keep one around for the occasional time I'm in the mood to wear it. I think this piece will just need a little experimenting for you to find the look that really captures the way *you* want to wear it.