Can help if you twist the prophecy. And I always liked The Horse and His Boy approach, in which Shasta/Cor didn't learn about the prophecy until after the fact.
But another technique is to have the choosing be ambiguous. You have signs and portents that could mean something special, but could, without being nonsense, just be coincidences. You have to put the interpretation in the mouths of people who will be taken seriously, but not too seriously. Sole survivor of a catastrophe works well. Or a remarkably convenient meeting with someone who knows something the hero needs to know. Or a vision that hints without laying out the details. Gets the effect in. If done well, it smooths over the rough edges of coincidence without dragging Destiny on stage. (Or the gods. I don't approve of dragging the gods onto the stage even for this.)
The other advantage of this technique is that you don't get to lay out the prophecy so that the Chosen One can (dully) carry it out as detailed. Yes, you survived the fire, and are obviously cut out for Some Purpose -- but what purpose? The apparition of the Golden Stag shows that you have divine favor, but what will that let you do? etc.