I have my signal generator ( 2 prong plug) plugged into a power strip,
I have my isolation transformer ( 3 prong plug) plugged into the same
power strip, I have my radio ( 2 prong plug) plugged into the isolation
transformer. I have the black lead, from the signal generator clipped to
the chassis of the radio. Do I need a wire from the radio chassis to the
third receptical hole (ground) on the power strip?
Thanks

Nope.

T.

You can if you want. This will protect you from any capacitive coupling through the transformer--you can always get a zing on AC sets even though the chassis isn't connected directly to the line (though this can also be due to a chassis to line cord condenser). If the generator doesn't have a connection to ground, then a connection from the radio chassis to ground may prove helpful. Make sure that the generator is transformer operated (most are).

Thomas