This is not a bad problem but does need to be handled by a competent repairman or it will get worse. At Master Furniture Service, Inc. we would remove the broken section, bring it into the shop and depending on the color and type of marble we would glue it with an epoxy that would be colored to match the color of the marble. Then the top would be dressed (polished) and the original sheen restored. I have restored marble that was broken into multiple pieces and though I can't say that the repairs were invisible most people wouldn't be able to tell that the piece had been repaired. In addition the repair is permanent.
Marion Sack
May 2011