Loud Screeching when Coasting at High Speed

I’m looking for a bit of help with the noise I’m encountering on my 2007 Specialized Allez Comp (I know I’m due for an upgrade). It’s been a faithful bike and I’ve taken good care to get tune ups, etc. However, this noise started occurring when going downhill or at higher speeds while coasting. It stops when I begin pedaling. I can’t tell if it’s something with the chain tension or if there’s an issue with the rear hub. Anyone heard this before? It’s annoying as hell!