A chaingun is a repeating firearm with a mechanically driven action rather than an automatic one. The "chain" refers to a drive-chain drawn off from the gun's motor but there are various other ways of driving. This mechanism actually pre-dates automatic weapons - the Gatling gun was driven by a manual crank. Most gatling style weapons remain driven to the present day, but there are plenty of driven single barrelled weapons as well.
In most cases driven weapons require more mechanical sophistication than automatic ones and aren't able to use their action to absorb recoil, but tend to be more resistant to stoppages and sometimes have the advantage of being able to adjust their rate of fire. In particular misfires will not normally cause a stoppage, making a driven weapon more tolerant of poor quality ammunition.