Rear tire has started rubbing frame at one spot Riding my bike within my suburban residential neighborhood, I felt a shock, like a snap although I don't think anything snapped, followed by a rubbing noise every few seconds. Pedaling and the brakes continued to work.

I pulled over and examined my bike, starting with the brakes, and discovered that the left side of the rear tire now rubs against the left chain stay at one spot, near the tube valve stem. The wheel/tire is perfectly centered everywhere else along its circumference, just not there.

I've had this bike for about a year (bought at Goodwill), and, aside from a break over the winter, I've been riding it at least once a week, and I can tell you that this didn't happen before.

I haven't done any hard riding recently; I've been taking it easy as I build back up from my winter break.

The tire is seated correctly on the rim, as far as I can tell.

I didn't count the spokes off one by one, but looking at where they each meet the rim, they seem to all still be intact. There weren't any dangling off or obviously snapped away.

The bicycle is an old Univega hybrid bike with 700c Bontrager tires. I'm no expert, but I'd describe the tires as road tires, about an inch wide.

I'm stumped for what's caused it or how to fix it.
Check the spokes - its likely one or more has broken ("I felt a shock, like a snap....".). The ones to check are ones that got from the rim, where the rubbing is occurring, to the hub on the opposite side of the rubbing (in your case, the right side of the hub). If these have let go, there is nothing stopping the rim being pulled to the left. 

It may be that these are loose, not broken, although it unlikely. If the spokes are not broken, you might be able to straighten the rim by tightening the right side spokes and if needed, loosening the left side ones. It's not too hard if the rim is not too far out of true, but needs patience for a novice. 

If there is a broken spoke, or the rim is a long way off and cannot be "tweaked" it will be worth taking to your LBS to get them to look at it. As it's only a year old, spokes should not be breaking.