Drying properly depends on what you washed it with. Start with going outside and holding the chain at the middle and spinning it around as fast as you can to spin out whatever you can. That will eject the liquid and any suspended dirt, otherwise simply drying it will only remove the liquid, but leave the dirt (dirt doesn't evaporate).

Now, for water based solvents, put it on a piece of aluminum foil and bake it on the oven at 200 for 10-20 minutes. You can't safely heat petroleum solvents because of the flammability, so put the chain on the windowsill in direct sun, to warm slightly and speed drying.. If you have something black to put it on so much the better since that will warm faster.

You can also dry a chain in the solar oven parked in your driveway. Put it on something on the dashboard, and leave a window cracked open an inch or so. Parked in the sun a car gets hot enough to dry either solvent or water washed chains within an hour or two. or less, but I err high to be safe).

Remember that the key to effective lubrication is to start with a clean, dry chain.
Then