| Chelsea FC v West Bromwich Albion FC 24/02/1960 | View match | |
| Sheffield Wednesday FC v Chelsea FC 27/02/1960 | View match | |
| Chelsea FC v Luton Town FC 05/03/1960 | View match | |
| Everton FC v Chelsea FC 12/03/1960 | View match | |
| Chelsea FC v Blackpool FC 19/03/1960 | View match | |
| Blackburn Rovers FC v Chelsea FC 30/03/1960 | £8.50 | |
| Chelsea FC v Manchester City FC 02/04/1960 | £9.50 | |
| Arsenal FC v Chelsea FC 09/04/1960 | £5.50 | |
| Chelsea FC v Tottenham Hotspur FC 15/04/1960 | View match | |
| Chelsea FC v Nottingham Forest FC 16/04/1960 | View match | |
| Tottenham Hotspur FC v Chelsea FC 18/04/1960 | View match | |
| Bolton Wanderers FC v Chelsea FC 23/04/1960 | View match |