As has been suggested:
Chain too tight.
Not enough or the wrong sort of lube.
Chain line.
New parts not playing nice.
Old parts not playing nice.
A bike that just likes to chat to itself when riding for no good reason (bit like my daughter)

Pick one. There's even a good chance you'll be chasing this until the bits are all worn out and you replace them with exactly the same bits whereupon it decides not to make any noise at all just to piss you off.

Seriously, check the above and if you can't find anything wrong, just chalk it up to part of the character of the bike.