Please tell us your setup:
Chainwheel make/model/width?
Chain make/model/width?
Cog make/model/width?
Bottom Bracket make/model?

Are you sure that it's the chain? It could be the bearings in your BB (if you have the looseball type). If you get the sound when you put your weight the bike or when climbing, then it's probably your BB. If it's loose ball, clean, grease, and repack them OR just use a sealed BB.

If you lift the rear of the bike and turn the crank arm with your hand and you hear a constant sound, then it's probably your chain/chainwheel combo.

What size are your chainring and cog, 3/32 or 1/8? If you have 3/32 try a 1/8 chain.

One more thing, what kind of chainring are you using? The cut of the teeth could be contributing to the noise. I upgraded my chainring and chain and reduced the sound of my bike significantly.