I've always liked the Chemex, but it has problems. First, it loses a lot of heat during extraction, and it is nearly impossible to keep a proper temperature for the duration of brewing. Second, the filter clogs easily with just about any grind setting. The only way around the clogging problem is to pour the water over the grounds in such a way that it keeps them near the outside of the upper regions of the filter, rather than forming a restrictive bed in the bottom of the cone. This also prevents an even extraction, however, which is perhaps the biggest problem with a Chemex.
Even with these limitations, the Chemex can still brew a very nice cup with great aromatic clarity, but the extraction quality often suffers. This results in a cup that lacks sweetness and acidity, accentuating bitter notes. Flavors are not fully developed, and the coffee just can't show everything it has to offer.
The solution? Use the Chemex only for what it does best; filtration. Brew the coffee in another vessel, where it can extract evenly at a constant, ideal temperature. The resulting cup has the same brilliant clarity that the Chemex is known to produce, but has the flavor, body, and balance of a proper extraction. Here's how I do it:
1) Preheat a thermally insulated carafe (or travel mug) with boiling water two times. A 1.3L Zojirushi vacuum insulated steel carafe (technically not designed for hot liquids) is perfect. This will be your brew chamber.
2) Put a filter in the Chemex, and rinse it with oceans of boiling water. That papery taste is persistent!
3) Grind the proper amount of coffee. Use a grind setting similar to what you would use for cupping (somewhat coarser than what most people use for automatic drip).
As far as strength goes, 62 grams per Liter of water is a good starting point. I use 45 grams of coffee and 725 grams with the 1.3L Zojirushi carafe and a six cup Chemex. You want your brew chamber to be nearly filled once the water and coffee are added.
4) Empty the preheat water from your brew vessel, and add your ground coffee. Using a scale, pour the proper mass of freshly heated (205 F) filtered water directly on top. Let the water mix and agitate the grounds as it is added. Do not stir or mix with anything else. Put the lid on your brew chamber, and set a timer for three minutes.
5) When your timer beeps, open the carafe and use a spoon to break the crust that has formed, and give the entire volume a gentle stir from top to bottom. Wait about thirty seconds so most of the grounds have a chance to settle to the bottom.
6) Slowly and gently pour the coffee from your carafe into the filter in your Chemex. The liquid leaving the carafe should be relatively clear, leaving most of the grounds behind. Stop pouring when fine grounds start to leave with the liquid.
Filtration will take about a minute. There is little risk of over extraction now that most of the grounds have been separated from the water.
7) When the filtration really slows down, remove the filter along with whatever small amount of grounds and liquid remains. Don't worry about letting every last drop of coffee come through. I usually lose about 10 - 20 ml of liquid when I take the filter out.
8) Enjoy a cup of coffee with great clarity of aroma and flavor, and all the sweetness that comes from a proper extraction. I dare you to find a better Chemex method.
9) Experiment to find the ideal grind setting, water temperature, grounds to water ratio, extraction time, etc... Do what tastes best to you, and remember that every coffee will have a different set of ideal parameters.