only when moving?
can you completely rule out an overtight chain, or a tight spot in the chain? are the sprockets (both of them) in good condition, or is one wearing oddly?
if you roll down the road, pull in the clutch and kill the engine, does the noise continue? (aka trans and chain still turning)
with the kill switch still off, let the clutch out (slowly) does the whine come in as the engine starts turning by the trans?