The Chemex website says that their glasses are dishwasher safe as long you take a few precautions [3].
First, be sure to remove the wooden collar/wooden handle and leather tie.
Then, ensure that you put the glasses in the dishwasher upside down so that the hot water can reach all the nooks and crannies.
Finally, don't use any detergent that is designed for stainless steel because it can damage the glass and cause chemical residues.