Can I stop voles with a barrier of marble chips around my hostas?

This will probably not work. Voles will dig under the chips. Two options work best: using a metal mesh barrier and planting your hostas in pots above the soil.

Related Videos:
Keep Voles at Bay: Building Wire Cages to Protect Your Plants
Vole Proofing and Planting Hostas

Related Resources:
Pest Alert – Those Voracious Voles!
Voles