There are no obvious Chailey related matches for this man, the closest being a Wallace Arthur Gibbs whose birth was registered at Lewes in 1872.
The National Archives yields two possibilities: 19485 Private (later Temporary Staff Sergeant) Arthur Gibbs of the 12th
, RAMC and 54609 Private Arthur
Gibbs. Of the two, I think the first man is probably the more likely candidate but further research is needed here. General Hospital