So the chain tends to slip/skip/suck/misbehave when you apply a lot of pressure at the pedals... perhaps your chainring teeth have worn down to the point where the chain is slipping centrifugally all the way around at the same time. I've had this happen with worn-out middle chainrings on my mountain bike, and it is a recipe for cut knees and bruised, um, body parts. If you happen to be blessed with a digital camera, could you post a close-up photograph of your chainrings? Or ask a trustworthy LBS for an opinion.
Another possible reason for slipping under power is that your chain is at a different stage of wear than the rest of your drivetrain (cogs and/or chainrings, particularly cogs).
If it is actually chain suck
happening under power, where the chain clings to the chainring and won't come off cleanly at the bottom, then this could be caused by burrs on the teeth or bent teeth. If you decide to replace chainrings, I strongly recommend aftermarket 7075 aluminum ones, and my favorites are Real's "Ultimate" ones. The aluminum is very hard, very strong, and nickel-plated. These things are worth the money!
Also, can you post more info on your bike? Could help...