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Chelsea matches where Arthur F Kirby was referee
| Date | Venue | Opponent | Score | Comp |
| 20/03/1920 | Stamford Bridge | The Wednesday | 1-1 | Football League Division 1 |
| 06/04/1920 | Hillsborough | The Wednesday | 2-0 | Football League Division 1 |
| 22/11/1924 | Horsley Hill | South Shields | 1-1 | Football League Division 2 |
| 20/04/1925 | Stamford Bridge | South Shields | 1-1 | Football League Division 2 |