The White Chisel is one of the eight companies that make up the Mining Consortium.
During The Giant Dwarf quest, you can choose to help this company by gathering materials, primarily ores and bars, for its head secretary. After which, you can do some tasks for the director. The director will then let you join the company as a member, so that you can choose him to have a stone head of his image carved onto the giant statue that is in the middle of Keldagrim.
Also, in Forgettable Tale of a Drunken Dwarf, one can ask the Director to help remove the boards blocking a railway tunnel.