Under the Queen it was the Marquess of Cholmondeley.
Not sure who the next one will be.
If I understand correctly, there are several possibilities of families who hold a small percentage of the office.
On the wikipedia I see that several women are also named as possible Lord Great Chamberlains (including the 28th Baroness Willoughby de Eresby). Could there be a female Lord Great Chamberlain? Or would the position go to the eldest son of a female holder of the position?