Why is oxygen the third most common element in the universe?

So it appears from several sources that the three most common elements in the universe are, in order, hydrogen, helium, and oxygen.

The first two make perfect sense to me. Hydrogen especially -- it's basically just a stray proton, right? Most of them have an electron buddy, of course, but it's not hard to see how that could happen. And then helium is two protons fused together, and as far as I understand it requires the lowest amount of energy to fuse. So that makes sense. You've got a universe full of stray protons (your most common element) and when they start to clump together producing heat and pressure, you fuse pairs of them together and get your second most common element.

But whence oxygen? It's #8 in the periodic table. My simple-minded imagination would have thought the order of frequency of elements would have been roughly the same as their atomic number, allowing some idiosyncracies for what's more stable, etc. And if it weren't, I would have expected the next most common to be maybe a noble gas, or just generally something with a distinct position in the periodic table. I can't see anything special about oxygen...

I'm assuming it has to do with some idiosyncrasy of stellar evolution. Can anybody help me out here?