I recently put together a Spicer/Kilo TT frame with all new parts put on it with a year of research gone into making sure the chainline would be straight and everything...and the drive chain makes a metallic whirring noise. I hastily convert an old 10-speed into a single speed bike buying only a shimano freewheel, and reusing everything else on the bike. Silent as a muther'ucker.

I need to get my new ride to quiet down.

meh, it happens, if you want silence ride w/ earplugs

How far off is your chainline? Is your chain, cog and crank all the same tooth size?
A clean "whirr" is nice.

I am assuming it's an aluminum frame. Aluminum frames make for noisy track bikes. It has something to do with how the chain noise resonates through the frame. I have had the exact same parts on two frames that really only differed in what they were made of... aluminum frame: noisy, steel frame: silent.
Such is life.

aluminum frames dont always make noisy track bikes. i just finished up a alu peugeot and its silent as can be.

Dude's got a Spicer/Kilo TT frame.

Lube the chain up real nice, loosen the tension a little.

check your chainring bolts.
if it's an old wheel, try cleaning and properly repacking your rear hub.

Thank you all for your suggestions. I'll try lubing it up and loosening the tension a bit. It's a brand new wheelset, so I don't think I need to pack anything.