Since the introduction of the Maxim gun in the late 19th Century, machine guns have relied on the recoil or the gas from the fired cartridge to cycle the action. When the power from cartridge is less than normal, for instance an underloaded or misfiring cartridge (it happens!) the gun jams and has to be cleared by the operator before the gun is back in action. To get around this and make the gun more reliable an electric motor is chained to the bolt to work the gun. The benefit is a gun that won't jam if a cartridge misfires, as the round is extracted by the electric motor and thrown out with the rest of the empty shells.
Chain guns have only one barrel and can be confused with Gatling guns which have many. They have an excellent reliabilty history, for example the Hughes EX-34, a 7.62 mm Nato rifle caliber gun, can easily go 100,000 rounds without a failure. Because the gun is operated by an electric motor, the gun can fire at different speeds which theoretically is only limited by the pressure drop in the barrel of the last round, and the reliability of the chain drive. The Hughes gun is rated at 570 rounds per minute, but they are trying to get the rate up to 1000 rounds per minute. This weapon has been adopted by the British Army for armored vehicles and tanks, and is known as the L94A1 chain gun
This also applies to bigger caliber guns, such as the 25mm autocannon in the Bradley Fighting Vehicle. These dual feed chain guns have taken out Soviet designed T-55 tanks in Iraq, and even T-72's at close range using tungsten armor piercing sabot rounds. This gun can fire 200 rounds a minute, And they get bigger. The Hughes M-230 30mm chain gun is used on the Apache helicopters and Special Forces Blackhawks. These guns cook at 650 rounds per minute using 2 horsepower electric motors. ATK and BAE make chain gun systems from 25mm, such as the M-38 Mod2 shipboard system and the M-242 Bushmaster gun in the Bradley, up to the 35mm Oerlikon and the 50mm SuperShot guns. The big 50 uses a 3 horsepower motor and weighs 500 pounds. The chain gun principle seems to have no limits.