I think someone VERY steady could probably cut chines with a circular saw, but I wouldn't do it. The bevel isn't the problem, it's cutting a piece that long and skinny and keeping it straight.
You can get a cheap table saw for a hundred dollars these days, and unless you are doing a lot of work, or trying to do extremely fancy work, a cheap table saw is all you need.
Safer, more accurate, way faster.
If I absolutely couldn't get a table saw... I think I'd improvise a way to clamp my circular saw upside down with an improvised fence and use it like a table saw. Not saying that's smart... but I've done it in a pinch on a jobsite when I had to.
For no more than you pay for a basic portable table saw, I really think it is the way to go. And once you have it, you will use it quite a bit.
George