Unclean and under lubricated drivetrain components can contribute to chain suck.
Running an old chain on new chain rings can cause this. The teeth on the chain ring might not line up exactly to a stretched chain, causing the chain to not release cleanly off the chainring. Plus, the old chain will greatly accelerate the wear on your chain rings.
A chain that was twisted in anyway might be prone to causing chainsuck as well. Lets say your chain was overshifted and fell off either the small or large chain ring, and you kept pedaling, jamming the chain between the derailleur and chain ring. A chain that has chain suck once might be more prone to having chain suck again as it may become twisted.
Another common cause of chain suck is an improper chainline. If a new bottom bracket was installed, the spindle size may not be correct.
If none of these suggestions help, several companies make anti-chainsuck devices, ask at your local bike shop. This device is a plate that is profiled to match your chain rings, bolted under your chain stays. If the chain starts to be sucked, it hits the plate and falls free again.
Cheers,
Juba