I had absolutely no idea what it was, so I posted the photo on Facebook and asked for help. This morning I found several replies. Thanks, everyone.
The concesus seemed to be swallow. BPaul gave me the family name, Hirundindae, and I soon found the Welcome Swallow (Hirundo neoxena):
Colour: metallic blue-black on top and light to dark grey on its breast and belly. Its forehead, throat and upper breast are rust in colour. It has grey legs and feet, and its eyes and bill are black.
That sounded close, but the throat color is off—but it's followed by this:
A young Welcome Swallow has shorter tail feathers than an adult and its forehead and throat are a creamy beige (instead of rust).
Swift: is larger and has longer and more-curved wings, and rarely lands. Welcome Swallows are commonly seen sitting on perches.
I'll keep looking, but I think what we have here is a young Welcome Swallow.
More, and lots of really good pics here.