ESD Protection on Un-grounded Chasis
Should I be doing the above step as the chassis is effectively not grounded?


Chassis ground is to protect against faults (shorts from power inside of the box to itself) and ESD. With low voltage DC it is not always necessary to protect against faults, with AC mains in a product it is and the mains voltages must be fused. 

If there is a fault, it is probably best for the fault current to return through the chassis so grounding the chassis to the ground of the supply is probably the best way to go. In the past I've done this at the input with a DC jack negative terminal connected right to the chassis.

One question I have is what will happen to your DC supply if ESD hits it, it should have certifications that it has been tested for ESD immunity. Again the best pathway is also ground.


  If its connected and there is ESD on the metal chasis, wouldn't the circuit get damaged as its connected to the Circuit GND at
  multiple points via mounting holes?


Electricity always returns to the source via the lowest impedance pathway, so if you shunt the current away from the PCB through the chassis and down the cable that is the best you can do. If you do need to star the ground on the PCB, try and do it as close to the power inlet as possible. 

You don't need to connect all of the mounting holes to the PCB ground (you can leave a 10's of mils gap around the mounting hole) just the one by the inlet could be connected to PCB ground (if its a DC jack mounted right to the board). If the PCB has a pigtail, then star the negative terminal on the chassis.