A couple more things:
* Remove the chainring, clean and grease the chainring bolts and flats. Also check to see how worn the chainring is – if it's sharktoothed, and you've not flipped it before, flip it.
* check the freewheel teeth too – if they are worn, then the teeth may be chainsucking the chain as you pedal hard – but it won't show if you're spinning.
Basically, if you've got a very worn drivetrain, and you've swapped to a brand new chain, it will make noise when you crank hard. It's really important, for this reason, to hang on to old chains. If you have a sprocket rather than a freewheel, it wouldn't hurt to try swapping to a new sprocket to see if the noise goes away. Also try comparing new chainrings (or other chainrings) to see how worn the ones on your singlespeed are.
HTH