It's never been clear to me what chambray is. Is it a denim shirt? Or is chambray something different?
I do have a light blue denim shirt, from BR. It's soft and comfy yet a little tailored and structured. Normally button downs don't work for me (too stiff & starched) but this works for me. As others mentioned, I love the juxtaposition of it pared with dressier clothes like tucked into a pencil skirt (brocade, lace, bright color), worn under a velvet blazer, etc. But mostly I like wearing it untucked over black ponte knit skinnies with fun ballet flats.
I don't wear jeans all that much, so this is an easy way to look casual and blend in when everyone else is wearing denim. For similar reason, I am apt to pop a jean jacket over everything.