As others have said, capital gains distributions (box 2a of a 1099-DIV) can be offset by either long or short term capital losses.
Capital gains distributions (box 2a of a 1099-DIV) are taxed at long term capital gains tax rates, some of which can be, for lower income people, 0%. I assume by "I have ordinary income well in excess of the capital gain distribution", you mean that you know that your Capital gains distributions will be subject to the 15% rate or higher. And, that is why you want to offset them with losses.
