Well the recipe I found. It is not hard at all. It just takes some time and attention. Like a Risotto.

To make the velouté, which is one of the 5 mother sauces:

1 Q plus a pint of high quality chicken stock. If you can't use home-made, use a good low or no salt broth because this is going to reduce a lot so it can become quite salty. The extra pint is to compensate for evaporation.
2 oz. flour (about 1/2 C, though it's a good idea to weigh it.)
2 oz. unsalted butter (1/2 a stick. Only have salted? See above and be warned.)

Get your stock into a stockpot and bring it to a simmer if it's cold.

In a skillet with rounded sides on medium heat, get your butter melted, then add your flour to create a roux. Keep stirring/whisking it until turns an ivory color and starts to smell like cookies. Gradually deglaze with some of your stock until it's incorporated and in no danger of clumping, then add your deglazed roux to your stock pot. Stir and simmer until the sauce has reduced a bit so you end up with a quart of sauce.

For the Supreme Sauce:

2T of unsalted butter, ideally clarified but not required
2T of shallots, minced
1/4C white wine
1/2C heavy cream
1Q Chicken Velouté
Kosher salt and pepper (use white pepper if you don't want the specks)
1/2 a lemon or so
2T cold butter, whole

Okay, here we go. Bring your velouté to a simmer. Sweat your shallots in the clarified butter until softened but not browned. Deglaze with the white wine and simmer until nearly dry (this is called au sec, if you see this term anywhere). Add the cream and reduce until it coats the back of a spoon. (This is called nappé, if you dip a spoon in your sauce and turn it sideways, you should be able to draw a line through it with your finger and have it maintain its shape.)

Add your shallot/cream mix to your now warm velouté and reduce GENTLY about 50% to around the nappé state. TASTE! Season. If you've used canned broth it may need no salt at all, add pepper to taste and a squirt of lemon juice will perk up the sauce, use your judgement.

If it's ready, remove it from the heat and whisk in your 2T of cold butter.

And just in case you don't have one...

Chicken Stock
Ingredients
4 pounds chicken carcasses, including necks and backs
1 large onion, quartered
4 carrots, peeled and cut in 1/2
4 ribs celery, cut in 1/2
1 leek, white part only, cut in 1/2 lengthwise
10 sprigs fresh thyme
10 sprigs fresh parsley with stems
2 bay leaves
8 to 10 peppercorns
2 whole cloves garlic, peeled
2 gallons cold water
Directions
Place chicken, vegetables, and herbs and spices in 12-quart stockpot. Set opened steamer basket directly on ingredients in pot and pour over water. Cook on high heat until you begin to see bubbles break through the surface of the liquid. Turn heat down to medium low so that stock maintains low, gentle simmer. Skim the scum from the stock with a spoon or fine mesh strainer every 10 to 15 minutes for the first hour of cooking and twice each hour for the next 2 hours. Add hot water as needed to keep bones and vegetables submerged. Simmer uncovered for 6 to 8 hours.

Strain stock through a fine mesh strainer into another large stockpot or heatproof container discarding the solids. Cool immediately in large cooler of ice or a sink full of ice water to below 40 degrees. Place in refrigerator overnight. Remove solidified fat from surface of liquid and store in container with lid in refrigerator for 2 to 3 days or in freezer for up to 3 months. Prior to use, bring to boil for 2 minutes. Use as a base for soups and sauces.

I have not tried the stock recipe as I always just throw together my own with what I got. I always use the mirepoix though. And Alton Brown is Awesome!