The simplest way to maintain a chain is to frequently wipe it down and then lubricate it. If you do this before or after every ride or two, your chain will stay clean, run smoothly, and last longer, without needing to use a solvent. To simplify this procedure, I recommend leaving a pair of rubber gloves, a rag, and some chain lube next to your bike. Whenever you return from a ride, put on the gloves, wipe and lube the chain, and put your bike away; the bike can be standing on the ground or in a bike stand. It takes maybe a minute, your hands stay clean, and your bike is ready for the next ride.
With a rag in your hand, grasp the lower length of the chain (between the bottom of the chainring and the lower jockey wheel of the rear derailleur). Turn the crank backward a number of revolutions, pulling the chain through the rag. Lubricate each chain roller by turning the crank and running the chain past the dripping tip of the chain-lube bottle. Wipe the chainrings, cogs, front derailleur, and jockey wheels while you’re at it, and the entire drivetrain will keep running smoothly.