GC hums with separated PS

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I built a non-inverted GC LM3875. The powersupply was separately housed and a 4 lead umblical cord was connect from it to the amp. I have one signal star ground and one power star ground in the amp; they are connected together with a thin wire. However, I didn't connect any of them to the amp chassis. My question is: is it necessary to connect them to the amp chassis? I don't know what it will do because the amp chassis was not earthed to the socket. What is the usual way to ground stuffs when the amp and powersupply were housed into separate chassis? I'm having audible hum. Thanks for your help

WC
 
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