Repairing an old Bench Power Supply
I think sstobbe is on the right track here - something in the supply likely has a “sneak path” to the chassis. I would start troubleshooting this by connecting a high value resistor (100 k perhaps) between the minus output and the chassis ground. That shouldn’t make the supply turn off and you can measure the voltage across the resistance- check for both AC and DC voltage. Since there shouldn’t be any voltage the amount may give you a hint of where the problem may be. 

You can also unplug the supply, make sure it is fully discharged and use an ohmmeter to check the resistance between various points of the board and chassis- they should all be high resistance (of course take the resistor mentioned above off first).