I am planning a big Thanksgiving-related cooking fest this weekend (I promise to give you more details soon), and last weekend, I deboned a chicken in preparation.
Rob was in charge of putting the bones directly in a stock pot with spices, carrots, celery and water for making stock. 
We let it simmer for a few hours and then put the whole thing in the fridge. I didn't take the bones out or strain the stock because I was just too dang tired. That evening, I was reading a cookbook called "Better Than Store-Bought ," which has a recipe for what it calls "chicken extract," but for modern clarity's sake, I will call chicken base. 
Basically, you strain and skim the heck out of your stock, and then cook it down so it's thick enough to coat a metal spoon. Then you store it in a jar in your fridge or freezer, and you can reconstitute it to make broth or soup. The cookbook also has a similar recipe for making beef base (well, "beef essence,") and even gives instructions for turning these items into homemade bouillon cubes.
I had some time at home Tuesday evening, so I decided to cook the chicken stock down to chicken base. It was easy, and I liked that the end result was so concentrated, it didn't take up much space. I constantly fight for space in our freezer, so it was nice to be able to store it in a small jar in the fridge. Plus, we're walking a fine line to poultry overdose at our house these days, so I also appreciated not having to make more chicken soup.
I must admit, though, I did not strain or skim the stock nearly as much as the directions indicate. Our base turned out a bit cloudy, but I think it should be OK. I reconstituted it to make some broth to include in our dinner last night, and it worked just fine.
Here's the cookbook's instructions. They are very detailed.
6 to 6 1/2 pounds of chicken necks and backs, with any loose fat removed
7 quarts water, or enough to cover the chicken by 2 inches
3 medium carrots, scrubbed and sliced
1 medium-large onion, stuck with two cloves
1 rib celery, with leaves, sliced
1 leek, roots and any discolored tops removed, slipt lengthwise and washed thoroughly
3 sprigs parsley
1 bay leave
1/4 teaspoon dried thyme
Rinse and drain chicken parts and put them into a stock pot. Add water. Bring to a boil and boil briskly, skimming off the foam as it rises, for five minutes, or until no more scum appears.
Add the rest of the ingredients and turn down heat until the liquid simmers gently, with the pot partly covered. Cook the chicken and vegetables three to four hours, or until they are very soft. Do not allow the pot to boil.
Strain off the broth, pressing down the debris in the sieve to extract all possible juices. Discard the solids, Skim the fat from the broth and return the broth to the rinsed-out pot.
Bring the stock to a simmer and let simmer uncovered until it has reduced by half.
Strain again, this time through a sieve linged with dampened cheesecloth. Rinse out the pot, return the broth and continue the reduction at a simmer, with the pot uncovered, skimming from time to time. (Note that the cooking and reduction needn't be a continuous process. At any point you may stop, let the stock cool, uncovered, and resume the cooking when it is convenient. Refrigerate the stock in warm weather, or, in cool weather, if you're holding it for more than eight hours.) (Editor's note: I'd probably only let it sit out for about two hours, personally, even in cooler weather.)
When stock has been reduced to about one quart, strain it again, either through a fine sieve or a coarser sieve lined with dampened, doubled cheesecloth. Resume the reduction, still at a steady simmer. Put it into a smaller pan (a wide, shallow one is best). This is the point at which you must begin to watch the cooking and stir the extract occasionally; don't let it scorch. Skim frequently to remove scum and fat from the top.
When the extract is thick enough to coat a metal spoon, pour it into clean, dry jars. Cool it at room temperature, uncovered, then cover the containers and refrigerate or freeze the extract. If frozen, scoop out with a hot spoon as needed.
Makes about 1 3/4 cups (reconstituted, about 7 quarts of stock) or 1 cup of stock per tablespoon of extract.
You can keep this "almost indefinitely in the freezer," the cookbook says. "Refrigerated, it will keep for a long time, but check now and then for mold (if any appears, cut it away with a hot spoon or knife blade.)
When you need extract for stock, dilute it (the stock will be pale golden brown) and use as you would chicken broth. The extract is deliberately left unsalted so that it can be used to enrich seasoned sauces or soups. If you wish to sip it neat, dissolve 1 tablespoon of extract with 1/4 teaspoon salt in a cup of boiling water.