Question: I plan to add some lighting in positions on the ceiling that doesn't have nearby wire available.

The there is no free space between the ceiling/roof in which to run a wire (there's the wood, then solid foam block insulation, then weather barrier, then the shingles). So, I would need to run wire (12/2 or 12/3) to that location somehow. I'm aware of Wiremold, but that wouldn't look very good with the style and material of the ceiling itself.

Is it possible, instead, to run the wire through a 0.5" channel routed out of a 1x1" piece of wood and affix that wood to the ceiling? I read through California electrical code (I'm in San Bernardino County, California), but didn't see anything specific around this (unless I missed it, or interpreted it incorrectly).

Thanks in advance.

Answer: 
No, you can't do it unless there's a "nail plate" to protect it from physical damage (nails).

You could mill it out to 15/16" and lay in EMT metal conduit. It has the thinnest wall of any conduit and will provide the needed physical protection. Use that either simply as a damage shield in the vulnerable area, or if able, as a full-on wiring method for the entire route.
Can't say 100% certain with respect to code, but I did something very similar, with agreement of my electrician. He fished NM cable from bathroom lighting up to attic and through a hole to peak of ceiling between kitchen and dining room, around 8 feet along ceiling, then into ceiling to get to middle of dining room for new chandelier. I covered the 8' section with a piece of molding from Home Depot and it looks like it was always there.