Big black ants? Sounds like carpenter ants. Not something to mess around with. We've been fighting them for years. What we've settled on is going with an "environmentally friendly" (by comparison) pest company. They do a full abatement every year, and come back (for free) if we get a new incursion before the contract is up. Which we always do. The stuff this company uses is supposedly more environmentally friendly than the standard fare, which is one of the reasons it's been an ongoing battle (cause we didn't take off and nuke the site from orbit, which is the only way to be sure). It's not cheap, though. Good luck.

Boric Acid mixed with a sugar solution!

You need to know what they eat. Meat? Sugar? Then mix that thing with the boric acid as mentioned above. (If they're not sugar ants, the sugar trap won't do any good!)

Peanut butter and honey and boric acid is another thing, if the ants aren't going for the sugar and prefer protein/fats.

Cinnamon and mint (peppermint ideally), traditionally. But if they are in fact Carpenter ants then you want to nuke them from space. Those fuckers don't fuck around.

Might be too late for this incursion (yep, boric acid solution plus their favorite food is your best bet,) but ants typically love the sweet stuff that seeps from peony buds. Plant the peonies away from the house and the ants will have a snack and you will have beautiful, heavenly scented flowers.

Boric Acid mixed with a sugar solution!

If you don't feel like rolling your own, this is what Terro is. It's as environmentally friendly as that sort of thing can possibly get, and it works better than ANYTHING ELSE. Seriously. No crazy-ass megatoxic ant-ma-geddon spray from your exterminator will work as well as a few well-placed Terro baits. If you can get an exterminator in the right mood, they'll actually admit it to you.

The big black ants are looking for water, and new homes. Cinnamon worked pretty well for me.

Get some diatomaceous earth. Sprinkle it around their nests, their trackways and in the corners. Totally non-toxic, but fatal to most insects (especially cockroaches!)

Seconding that they're probably in the kitchen because of the availability of water. Wipe down the counters and sink as soon they get wet.

At my house, this problem is at its worst right now. They're looking for new places to live. If they like a certain area of your house, it can indicate dampness troubles. Once Spring is over, they seem to settle down.

if you can't find boric acid, just go to the detergent aisle in your grocery store and get a box of borax . the '20 mule team' is hell on ants .