This depends on the grit.
Chromium oxide is only a substance which is harder than steel. The size of the particles in the stone will dictate the grit and thus the effectiveness of the stone as a razor hone. Did you mean any stone in particular (manufacturer and model)? I've only ever seen one and it was in the 4000 grit range.
i've never heard of a chromium oxide hone either. awhile ago i asked about the bonding agents used in making hones when i had the idea that one could potentially use a crapload of chromium oxide and bonding agent to make a very very very fine hone...never tried it though