Can airborne floating/flying islands be scientifically possible?

I'm sure that this has been asked before, but I need floating islands for a fiction story I'm writing. It takes place 5000 years after a catastrophic event (on a vaguely earth-like planet populated with humans) that shrouded the surface of the planet in a continual fog of toxic, biochemically unstable gas a few kilometres thick.

Due to one reason or another, several thousand chunks of land were torn from the planet's surface and thrust into the upper atmosphere, carrying a few humans along for the ride. So, here is my question:

How could these landmasses be held in place for significant millennia without magical magnetic crystals or anything that breaches the realm of reality? The bending of physical laws and space-time continuum stuff is all fair game though.

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Can airborne floating/flying islands be scientifically possible?

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